Publications | Mahir Bilen Can

2026

Mixing and Merging Metric Spaces Using Directed Graphs

Mahir Bilen Can and S. Chakrabartty

2026

Submitted

Bib

Horospherical Schubert Varieties

Mahir Bilen Can, S. Kannan, and P. Saha

2026

Submitted

Bib

Evaluation Codes in Bottleneck Metrics

Mahir Bilen Can, D. Montero, and F. Özbudak

2026

Submitted

Bib

Double Coset Schur Rings and Diagonal Subgroups

Mahir Bilen Can and J. Rainbolt

2026

Submitted

Bib

Applications of Bruhat-Chevalley-Renner Decomposition to Metric-Aware Code-Based Cryptography

Mahir Bilen Can and Eli Coe Naig

2026

Submitted. Cryptology ePrint Archive, Paper 2026/665

Abs Bib HTML

We introduce metric-aware code-based cryptography by moving beyond the Hamming metric to the Niederreiter-Rosenbloom-Tsfasman (NRT) and sum-rank metrics and by exploiting their linear isometry groups via Bruhat-Chevalley-Renner decompositions. On the structural side, we give isometry-invariant distance tests: a parity-check prefix-rank test for single-chain NRT, its multi-prefix extension for block-NRT, and a block rank-profile test for sum-rank. We also analyze orbit structure under the relevant isometry subgroups and prove NP-hardness of a block-NRT canonicalization problem via a reduction from Exact-3-Cover, pinning down the difficulty of public "structure recovery." On the design side, we propose an inner-outer Niederreiter cryptosystem that couples a short rowwise single-chain NRT inner code with k_V outer binary Goppa codes across columns. For the resulting matrix code we prove a distance guarantee d_\mathrmNRT \ge \delta_V ⋅\min_t d^(t) and give a simple two-stage decoder (outer Goppa per coordinate, then inner per column). Public keys are dense, obfuscated parity-checks M = S H_\mathrmsys (PD) drawn from a metric-preserving subgroup, preserving decodability while hiding structure. Finally, we reduce NRT and sum-rank syndrome decoding to classical Hamming/Rank decoding, yielding one-wayness of the public syndrome map at standard regimes.
@unpublished{can2026bruhat, author = {Can, Mahir Bilen and Naig, Eli Coe}, title = {Applications of Bruhat-Chevalley-Renner Decomposition to Metric-Aware Code-Based Cryptography}, year = {2026}, note = {Submitted. Cryptology ePrint Archive, Paper 2026/665}, }

On the Homogeneous Space of a Pair of Associative Composition Algebras

Mahir Bilen Can, A. Casimiro, and F. Özbudak

2026

Submitted

Bib

@unpublished{can2026homogeneous,
  author = {Can, Mahir Bilen and Casimiro, A. and {\"O}zbudak, F.},
  title = {On the Homogeneous Space of a Pair of Associative Composition Algebras},
  year = {2026},
  note = {Submitted}
}

DCC
Generalized Hyperderivative Reed-Solomon Codes

Mahir Bilen Can and B. Horowitz

Designs, Codes and Cryptography, 2026

Abs DOI Bib

This article introduces Generalized Hyperderivative Reed–Solomon codes (GHRS codes), which generalize NRT Reed–Solomon codes. Its main results are as follows: (1) every GHRS code is MDS, (2) the dual of a GHRS code is also an GHRS code, (3) determine subfamilies of GHRS codes whose members are low-density parity-check codes (LDPCs), and (4) determine a family of GHRS codes whose members are quasi-cyclic. We point out that there are GHRS codes having all of these properties.
@article{can2026hyperderivative, author = {Can, Mahir Bilen and Horowitz, B.}, title = {Generalized Hyperderivative Reed-Solomon Codes}, journal = {Designs, Codes and Cryptography}, volume = {94}, number = {4}, pages = {91}, year = {2026}, doi = {10.1007/s10623-026-01849-3} }
DCC
MDS Stabilizer Poset Codes

Mahir Bilen Can

Designs, Codes and Cryptography, 2026

Abs DOI Bib

Poset metrics in the context of stabilizer codes are investigated. We establish a Singleton-type bound for stabilizer poset codes and introduce the notion of MDS stabilizer poset codes. Several characterizations of these codes are obtained, including criteria in terms of additive codes and perfect codes. We also prove existence results for large families of examples, thereby extending classical results on MDS poset codes to the quantum setting.
@article{can2026mds, author = {Can, Mahir Bilen}, title = {MDS Stabilizer Poset Codes}, journal = {Designs, Codes and Cryptography}, volume = {94}, number = {8}, year = {2026}, doi = {10.1007/s10623-025-01743-4}, }

FFA

Corrigendum to “Higher Grassmann Codes II” [Finite Fields Appl. 89 (2023) 102211]

Mahir Bilen Can, R. Joshua, and G. V. Ravindra

Finite Fields and Their Applications, 2026

DOI Bib

@article{can2026corrigendum,
  author = {Can, Mahir Bilen and Joshua, R. and Ravindra, G. V.},
  title = {Corrigendum to ``Higher Grassmann Codes II'' [Finite Fields Appl. 89 (2023) 102211]},
  journal = {Finite Fields and Their Applications},
  year = {2026},
  doi = {10.1016/j.ffa.2025.102700}
}

2025

Error Correcting Codes from General Linear Groups

Mahir Bilen Can

Journal of Algebra and Its Applications, 2025

Abs DOI arXiv Bib

The parameters of the AG codes on general linear groups are found. The hyperplane sections having the minimum (or maximum) number of rational points are determined.
@article{can2025error, author = {Can, Mahir Bilen}, title = {Error Correcting Codes from General Linear Groups}, journal = {Journal of Algebra and Its Applications}, year = {2025}, doi = {10.1142/S0219498825410324}, }

IEEE TIT

Higher Grassmann Codes III: Their Decoding and Quantum Variants

Mahir Bilen Can and R. Joshua

IEEE Transactions on Information Theory, 2025

DOI Bib

@article{can2025higher,
  author = {Can, Mahir Bilen and Joshua, R.},
  title = {Higher Grassmann Codes III: Their Decoding and Quantum Variants},
  journal = {IEEE Transactions on Information Theory},
  year = {2025},
  doi = {10.1109/TIT.2025.3596479},
}

Sigma
K-Orbit Closures and Hessenberg Varieties

Mahir Bilen Can, M. Precup, J. Shareshian, and Ö. Uğurlu

Forum of Mathematics, Sigma, 2025

Abs DOI Bib

This article explores the relationship between Hessenberg varieties associated with semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the general linear group. We establish the specific conditions under which these semisimple Hessenberg varieties are irreducible. We determine the dimension of each irreducible Hessenberg variety under consideration and show that the number of such varieties is a Catalan number. We then apply a theorem of Brion to compute a polynomial representative for the cohomology class of each such variety. Additionally, we calculate the intersections of a standard (Schubert) hyperplane section of the flag variety with each of our Hessenberg varieties and prove that this intersection possesses a cohomological multiplicity-free property.
@article{can2025korbit, author = {Can, Mahir Bilen and Precup, M. and Shareshian, J. and U{\u g}urlu, {\"O}.}, title = {K-Orbit Closures and Hessenberg Varieties}, journal = {Forum of Mathematics, Sigma}, volume = {13}, pages = {e103}, year = {2025}, doi = {10.1017/fms.2025.10063}, }

FFA

Shortest-Path and Antichain Metrics

Mahir Bilen Can and D. Montero

Finite Fields and Their Applications, 2025

DOI Bib

@article{can2025shortest,
  author = {Can, Mahir Bilen and Montero, D.},
  title = {Shortest-Path and Antichain Metrics},
  journal = {Finite Fields and Their Applications},
  volume = {108},
  pages = {102658},
  year = {2025},
  doi = {10.1016/j.ffa.2025.102658}
}

Toric Richardson Varieties

Mahir Bilen Can and P. Saha

Communications in Algebra, 2025

DOI Bib

@article{can2025toric,
  author = {Can, Mahir Bilen and Saha, P.},
  title = {Toric Richardson Varieties},
  journal = {Communications in Algebra},
  volume = {53},
  number = {5},
  pages = {1770-1790},
  year = {2025},
  doi = {10.1080/00927872.2024.2422028}
}

Nearly Toric Schubert Varieties of Type A

Mahir Bilen Can and N. Diaz Morera

Turkish Journal of Mathematics, 2025

Abs DOI Bib

A notion of a nearly toric variety is introduced. The examples of nearly toric varieties in the context of Schubert varieties are discussed. In particular, combinatorial characterizations of the smooth and singular nearly toric Schubert varieties are found. Furthermore, the counts and generating series are determined. Additionally, a connection between Dyck paths and a certain family of nearly toric Schubert varieties is established.
@article{can2025nearly, author = {Can, Mahir Bilen and Diaz Morera, N.}, title = {Nearly Toric Schubert Varieties of Type A}, journal = {Turkish Journal of Mathematics}, volume = {49}, pages = {Article 6}, year = {2025}, doi = {10.55730/1300-0098.3574} }

2024

Bounding the Sum of μ-Invariants on Pair Symbol Weights over Some Irreducible Codes

Mahir Bilen Can and F. Özbudak

In 26th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Cambridge, UK, 2024

Bib

@inproceedings{can2024bounding,
  author = {Can, Mahir Bilen and {\"O}zbudak, F.},
  title = {Bounding the Sum of $\mu$-Invariants on Pair Symbol Weights over Some Irreducible Codes},
  booktitle = {26th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Cambridge, UK},
  year = {2024}
}

Irreducible Unipotent Numerical Monoids

Mahir Bilen Can and N. Sakran

Semigroup Forum, 2024

DOI Bib

@article{can2024irreducible,
  author = {Can, Mahir Bilen and Sakran, N.},
  title = {Irreducible Unipotent Numerical Monoids},
  journal = {Semigroup Forum},
  volume = {109},
  number = {2},
  pages = {243-278},
  year = {2024},
  doi = {10.1007/s00233-024-10442-5},
}

DCC

Defects of Codes from Higher Dimensional Algebraic Varieties

Mahir Bilen Can, R. Joshua, and G. V. Ravindra

Designs, Codes and Cryptography, 2024

DOI Bib

@article{can2024defects,
  author = {Can, Mahir Bilen and Joshua, R. and Ravindra, G. V.},
  title = {Defects of Codes from Higher Dimensional Algebraic Varieties},
  journal = {Designs, Codes and Cryptography},
  volume = {92},
  number = {2},
  pages = {477-494},
  year = {2024},
  doi = {10.1007/s10623-023-01317-2},
}

On Generalized Wilf Conjectures

Mahir Bilen Can and N. Sakran

Portugaliae Mathematica, 2024

Abs DOI Bib

We investigate complement-finite submonoids of the monoid of nonnegative integer points of a unipotent linear algebraic group G . These monoids are in general noncommutative but they specialize to the generalized numerical monoids of Cisto et al.. We show that every unipotent numerical monoid has a unique finite minimal generating set. We propose a generalization of the Wilf conjecture in our setting. We contrast our Wilf conjecture against the generalized Wilf conjecture. Then we isolate two new families of unipotent numerical monoids called the thick and the thin unipotent numerical monoids. We prove that our Wilf conjecture holds for every thick (commutative) unipotent numerical monoid. Under additional assumptions on the conductors, we prove that our Wilf conjecture holds for every thin (commutative) unipotent numerical monoid.
@article{can2024wilf, author = {Can, Mahir Bilen and Sakran, N.}, title = {On Generalized Wilf Conjectures}, journal = {Portugaliae Mathematica}, volume = {81}, number = {1-2}, pages = {21-55}, year = {2024}, doi = {10.4171/pm/2112} }
Locally Semialgebraic Superspaces and Nash Supermanifolds

Mahir Bilen Can

In A Glimpse into Geometric Representation Theory, 2024

Abs DOI Bib

In this article, we present a novel theory of locally semialgebraic superspaces along with Nash supermanifolds. By adapting Batchelor’s theorem to our framework, we show that all locally semialgebraic superspaces and affine Nash supermanifolds can be derived from appropriate vector bundles. Our analysis of Nash supermanifolds involves an investigation of a topology, where closed sets are defined by Nash subsets. Within this context, we establish the softness of the structure sheaf for an affine Nash manifold. Moreover, we establish that under this topology, the higher cohomology of quasi-coherent sheaves on an affine Nash manifold vanishes completely. These results open up new directions for cohomological studies on Nash manifolds.
@incollection{can2024locally, author = {Can, Mahir Bilen}, title = {Locally Semialgebraic Superspaces and Nash Supermanifolds}, booktitle = {A Glimpse into Geometric Representation Theory}, series = {Contemporary Mathematics}, volume = {804}, publisher = {American Mathematical Society}, pages = {53-86}, year = {2024}, doi = {10.1090/conm/804/16111} }

A Glimpse into Geometric Representation Theory

2024

Bib

@book{can2024glimpse,
  editor = {Can, Mahir Bilen and Feldvoss, J{\"o}rg},
  title = {A Glimpse into Geometric Representation Theory},
  series = {Contemporary Mathematics},
  volume = {804},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2024},
  isbn = {978-1-4704-7090-6}
}

2023

Applications of Homogeneous Fiber Bundles to the Schubert Varieties

Mahir Bilen Can and P. Saha

Geometriae Dedicata, 2023

DOI Bib

@article{can2023applications,
  author = {Can, Mahir Bilen and Saha, P.},
  title = {Applications of Homogeneous Fiber Bundles to the Schubert Varieties},
  journal = {Geometriae Dedicata},
  volume = {217},
  pages = {Paper 103},
  year = {2023},
  doi = {10.1007/s10711-023-00786-1}
}

FFA

Higher Grassmann Codes, II

Mahir Bilen Can, R. Joshua, and G. V. Ravindra

Finite Fields and Their Applications, 2023

DOI Bib

@article{can2023higher,
  author = {Can, Mahir Bilen and Joshua, R. and Ravindra, G. V.},
  title = {Higher Grassmann Codes, II},
  journal = {Finite Fields and Their Applications},
  volume = {89},
  pages = {102211},
  year = {2023},
  doi = {10.1016/j.ffa.2023.102211}
}

Idempotent Varieties of Incidence Monoids and Bipartite Posets

Mahir Bilen Can, A. Casimiro, and A. Malheiro

Algebras and Representation Theory, 2023

DOI Bib

@article{can2023idempotent,
  author = {Can, Mahir Bilen and Casimiro, A. and Malheiro, A.},
  title = {Idempotent Varieties of Incidence Monoids and Bipartite Posets},
  journal = {Algebras and Representation Theory},
  volume = {26},
  number = {5},
  pages = {1975-2000},
  year = {2023},
  doi = {10.1007/s10468-022-10162-1}
}

2022

Asymptotic Semigroups and Two-Sided Weak Orders

Mahir Bilen Can

Journal of Algebra, 2022

DOI Bib

@article{can2022asymptotic,
  author = {Can, Mahir Bilen},
  title = {Asymptotic Semigroups and Two-Sided Weak Orders},
  journal = {Journal of Algebra},
  volume = {610},
  pages = {338-365},
  year = {2022},
  doi = {10.1016/j.jalgebra.2022.07.021}
}

A Catalanization Map on the Symmetric Group

Mahir Bilen Can, L. Nelson, and K. Treat

Enumerative Combinatorics and Applications, 2022

DOI Bib

@article{can2022catalanization,
  author = {Can, Mahir Bilen and Nelson, L. and Treat, K.},
  title = {A Catalanization Map on the Symmetric Group},
  journal = {Enumerative Combinatorics and Applications},
  volume = {2},
  number = {4},
  pages = {Article S4PP7},
  year = {2022},
  doi = {10.54550/ECA2022V2S4PP7}
}

Algebraic Groups in Action

Mahir Bilen Can

In Proceedings of the Gökova Geometry-Topology Conference 2021, 2022

Bib

@inproceedings{can2022algebraic,
  author = {Can, Mahir Bilen},
  title = {Algebraic Groups in Action},
  booktitle = {Proceedings of the G{\"o}kova Geometry-Topology Conference 2021},
  publisher = {G{\"o}kova Geometry/Topology Conference (GGT)},
  year = {2022},
  isbn = {978-1-57146-415-6}
}

Adjoint Representations of the Symmetric Group

Mahir Bilen Can and Miles Jones

In Proceedings of the 12th ISAAC Congress (Trends in Mathematics), 2022

Bib

@inproceedings{can2022adjoint,
  author = {Can, Mahir Bilen and Jones, Miles},
  title = {Adjoint Representations of the Symmetric Group},
  booktitle = {Proceedings of the 12th ISAAC Congress (Trends in Mathematics)},
  publisher = {Birkh{\"a}user},
  year = {2022}
}

2021

FFA

Higher Grassmann Codes

Mahir Bilen Can, R. Joshua, and G. V. Ravindra

Finite Fields and Their Applications, 2021

DOI Bib

@article{can2021higher,
  author = {Can, Mahir Bilen and Joshua, R. and Ravindra, G. V.},
  title = {Higher Grassmann Codes},
  journal = {Finite Fields and Their Applications},
  volume = {76},
  pages = {101905},
  year = {2021},
  doi = {10.1016/j.ffa.2021.101905}
}

Incidence Monoids: Automorphisms and Complexity

Mahir Bilen Can

Semigroup Forum, 2021

DOI Bib

@article{can2021incidence,
  author = {Can, Mahir Bilen},
  title = {Incidence Monoids: Automorphisms and Complexity},
  journal = {Semigroup Forum},
  volume = {103},
  number = {2},
  pages = {414-438},
  year = {2021},
  doi = {10.1007/s00233-021-10199-6}
}

Strong Gelfand Subgroups of F ≀S_n

Mahir Bilen Can, Y. She, and L. Speyer

International Journal of Mathematics, 2021

Abs DOI arXiv Bib

The multiplicity-free subgroups (strong Gelfand subgroups) of wreath products are investigated. Various useful reduction arguments are presented. In particular, we show that for every finite group F, the wreath product F ≀S_λ, where S_λis a Young subgroup, is multiplicity-free if and only if λis a partition with at most two parts, the second part being 0, 1, or 2. Furthermore, we classify all multiplicity-free subgroups of hyperoctahedral groups. Along the way, we derive various decomposition formulas for the induced representations from some special subgroups of hyperoctahedral groups.
@article{can2021strong, author = {Can, Mahir Bilen and She, Y. and Speyer, L.}, title = {Strong Gelfand Subgroups of $F \wr S_n$}, journal = {International Journal of Mathematics}, volume = {32}, number = {2}, pages = {2150010}, year = {2021}, doi = {10.1142/S0129167X21500105}, }

Diagonal Orbits in a Type A Double Flag Variety of Complexity One

Mahir Bilen Can and T. Le

Order, 2021

DOI Bib

@article{can2021diagonal,
  author = {Can, Mahir Bilen and Le, T.},
  title = {Diagonal Orbits in a Type A Double Flag Variety of Complexity One},
  journal = {Order},
  volume = {38},
  pages = {97-110},
  year = {2021},
  doi = {10.1007/s11083-020-09530-7}
}

2020

On the Borel Submonoid of a Symplectic Monoid

Mahir Bilen Can, H. Houser, and C. Wolfe

Advances in Applied Mathematics, 2020

DOI Bib

@article{can2020borel,
  author = {Can, Mahir Bilen and Houser, H. and Wolfe, C.},
  title = {On the Borel Submonoid of a Symplectic Monoid},
  journal = {Advances in Applied Mathematics},
  volume = {120},
  pages = {102073},
  year = {2020},
  doi = {10.1016/j.aam.2020.102073}
}

Toroidal Schubert Varieties

Mahir Bilen Can, R. Hodges, and V. Lakshmibai

Algebras and Representation Theory, 2020

Bib

@article{can2020toroidal,
  author = {Can, Mahir Bilen and Hodges, R. and Lakshmibai, V.},
  title = {Toroidal Schubert Varieties},
  journal = {Algebras and Representation Theory},
  volume = {23},
  number = {5},
  pages = {1927-1943},
  year = {2020}
}

Stirling Posets

Mahir Bilen Can and Y. Cherniavsky

Israel Journal of Mathematics, 2020

DOI Bib

@article{can2020stirling,
  author = {Can, Mahir Bilen and Cherniavsky, Y.},
  title = {Stirling Posets},
  journal = {Israel Journal of Mathematics},
  volume = {237},
  number = {1},
  pages = {185-219},
  year = {2020},
  doi = {10.1007/s11856-020-2004-1}
}

The Bruhat-Chevalley-Renner Order on the Set Partitions

Mahir Bilen Can and Y. Cherniavsky

Séminaire Lotharingien de Combinatoire, 2020

Bib

@article{can2020bruhat,
  author = {Can, Mahir Bilen and Cherniavsky, Y.},
  title = {The Bruhat-Chevalley-Renner Order on the Set Partitions},
  journal = {S{\'e}minaire Lotharingien de Combinatoire},
  volume = {84B},
  pages = {Art. 64, 11 pp.},
  year = {2020}
}

Sects

Mahir Bilen Can and Aram Bingham

Journal of Algebra, 2020

Bib

Remarks on Enveloping Semigroups

Mahir Bilen Can

Communications in Algebra, 2020

Bib

@article{can2020remarks,
  author = {Can, Mahir Bilen},
  title = {Remarks on Enveloping Semigroups},
  journal = {Communications in Algebra},
  volume = {48},
  number = {5},
  pages = {2092-2109},
  year = {2020}
}

arXiv
On the Fixed Points of a Regular Unipotent Element

Mahir Bilen Can

arXiv preprint, 2020

Abs arXiv Bib

The fixed point variety of a regular unipotent element on a wonderful completion is investigated. For the wonderful completion of the quotient by a symmetric Levi subgroup, it is shown that the fixed point variety is SL_2-regular.
@article{can2020fixed, author = {Can, Mahir Bilen}, title = {On the Fixed Points of a Regular Unipotent Element}, journal = {arXiv preprint}, year = {2020}, }

2019

Sigma

A Filtration on Equivariant Borel-Moore Homology

Mahir Bilen Can, Aram Bingham, and Yıldıray Ozan

Forum of Mathematics, Sigma, 2019

Bib

@article{can2019filtration,
  author = {Can, Mahir Bilen and Bingham, Aram and Ozan, Y{\i}ld{\i}ray},
  title = {A Filtration on Equivariant Borel-Moore Homology},
  journal = {Forum of Mathematics, Sigma},
  volume = {7},
  pages = {e18},
  year = {2019}
}

The Rook Monoid Is Lexicographically Shellable

Mahir Bilen Can

European Journal of Combinatorics, 2019

Bib

@article{can2019rook,
  author = {Can, Mahir Bilen},
  title = {The Rook Monoid Is Lexicographically Shellable},
  journal = {European Journal of Combinatorics},
  volume = {81},
  pages = {265-275},
  year = {2019}
}

A Geometric Interpretation of the Intertwining Number

Mahir Bilen Can, Y. Cherniavsky, and M. Rubey

Electronic Journal of Combinatorics, 2019

Bib

@article{can2019geometric,
  author = {Can, Mahir Bilen and Cherniavsky, Y. and Rubey, M.},
  title = {A Geometric Interpretation of the Intertwining Number},
  journal = {Electronic Journal of Combinatorics},
  volume = {26},
  number = {2},
  year = {2019}
}

The Genesis of Involutions (Polarizations and Lattice Paths)

Mahir Bilen Can and Özlem Uğurlu

Discrete Mathematics, 2019

Bib

@article{can2019genesis,
  author = {Can, Mahir Bilen and U{\u g}urlu, {\"O}zlem},
  title = {The Genesis of Involutions (Polarizations and Lattice Paths)},
  journal = {Discrete Mathematics},
  volume = {342},
  pages = {201-216},
  year = {2019}
}

Monoid Embeddings of Symmetric Varieties

Mahir Bilen Can, R. Howe, and L. Renner

Colloquium Mathematicum, 2019

Bib

@article{can2019monoid,
  author = {Can, Mahir Bilen and Howe, R. and Renner, L.},
  title = {Monoid Embeddings of Symmetric Varieties},
  journal = {Colloquium Mathematicum},
  volume = {157},
  number = {1},
  pages = {17-33},
  year = {2019}
}

Classification of Reductive Monoid Spaces over an Arbitrary Field

Mahir Bilen Can

In Advances in Algebra, 2019

Bib

@incollection{can2019classification,
  author = {Can, Mahir Bilen},
  title = {Classification of Reductive Monoid Spaces over an Arbitrary Field},
  booktitle = {Advances in Algebra},
  series = {Springer Proceedings in Mathematics \& Statistics},
  volume = {277},
  publisher = {Springer, Cham},
  pages = {67-94},
  year = {2019}
}

arXiv
The Betti Numbers of a Determinantal Variety

Mahir Bilen Can

arXiv preprint, 2019

Abs arXiv Bib

We determine the Poincaré polynomial of the determinantal variety det = 0 in the projective space associated with the monoid of ntimes n matrices.
@article{can2019betti, author = {Can, Mahir Bilen}, title = {The Betti Numbers of a Determinantal Variety}, journal = {arXiv preprint}, year = {2019}, }

2018

Loop-Augmented Forests and a Variant of Foulkes’ Conjecture

Mahir Bilen Can and Jeff Remmel

Algebraic Combinatorics, 2018

Bib

@article{can2018loop,
  author = {Can, Mahir Bilen and Remmel, Jeff},
  title = {Loop-Augmented Forests and a Variant of Foulkes' Conjecture},
  journal = {Algebraic Combinatorics},
  volume = {1},
  number = {5},
  pages = {573-601},
  year = {2018}
}

Wonderful Symmetric Varieties and Schubert Polynomials

Mahir Bilen Can, M. Joyce, and B. Wyser

Ars Mathematica Contemporanea, 2018

Bib

@article{can2018wonderful,
  author = {Can, Mahir Bilen and Joyce, M. and Wyser, B.},
  title = {Wonderful Symmetric Varieties and Schubert Polynomials},
  journal = {Ars Mathematica Contemporanea},
  volume = {15},
  number = {2},
  year = {2018}
}

Counting Borel Orbits in Symmetric Varieties of Types BI and CII

Mahir Bilen Can and Özlem Uğurlu

Arnold Mathematical Journal, 2018

Bib

@article{can2018counting,
  author = {Can, Mahir Bilen and U{\u g}urlu, {\"O}zlem},
  title = {Counting Borel Orbits in Symmetric Varieties of Types BI and CII},
  journal = {Arnold Mathematical Journal},
  volume = {4},
  number = {2},
  pages = {213-250},
  year = {2018}
}

The Cross-Section of a Spherical Double Cone

Mahir Bilen Can

Advances in Applied Mathematics, 2018

Bib

@article{can2018cross,
  author = {Can, Mahir Bilen},
  title = {The Cross-Section of a Spherical Double Cone},
  journal = {Advances in Applied Mathematics},
  volume = {101},
  pages = {215-231},
  year = {2018}
}

A Representation on Labeled Rooted Forests

Mahir Bilen Can

Communications in Algebra, 2018

Bib

@article{can2018representation,
  author = {Can, Mahir Bilen},
  title = {A Representation on Labeled Rooted Forests},
  journal = {Communications in Algebra},
  volume = {46},
  number = {10},
  pages = {4273-4291},
  year = {2018}
}

arXiv
Ansatz for (-1)^n-1 ∇p_n

Mahir Bilen Can, Soumya D Banerjee, and Adriano Garsia

arXiv preprint, 2018

Abs arXiv Bib

We construct a special family of equivariant coherent sheaves on the Hilbert scheme on n-points in the affine plane. The equivariant Euler characteristic of these sheaves are closely related to the symmetic functions (-1)^n-1 nabla p_n. We prove a higher cohomology vanishing result of these sheaves. It follows from the Bridgeland-King-Reid correspondence that there is an effective S_n module underlying the aforementioned family of symmetric functions.
@article{can2018ansatz, author = {Can, Mahir Bilen and Banerjee, Soumya D and Garsia, Adriano}, title = {Ansatz for $(-1)^{n-1} \nabla p_n$}, journal = {arXiv preprint}, year = {2018}, }
arXiv
Sphericity of Smooth Schubert Varieties

Mahir Bilen Can and Reuven Hodges

arXiv preprint, 2018

Abs arXiv Bib

We consider the action of the Levi subgroup of a parabolic subgroup that stabilizes a Schubert variety. We show that a smooth Schubert variety is a homogeneous space for a parabolic subgroup, or it has a smooth Schubert divisor. Further, we show that all smooth Schubert varieties in a (partial) flag variety of a rank two simple algebraic group are spherical.
@article{can2018sphericity, author = {Can, Mahir Bilen and Hodges, Reuven}, title = {Sphericity of Smooth Schubert Varieties}, journal = {arXiv preprint}, year = {2018}, }

2017

Complex G_2 and Associative Grassmannian

Mahir Bilen Can and S. Akbulut

Journal of Gökova Geometry Topology, 2017

Bib

@article{can2017complex,
  author = {Can, Mahir Bilen and Akbulut, S.},
  title = {Complex $G_2$ and Associative Grassmannian},
  journal = {Journal of G{\"o}kova Geometry Topology},
  volume = {11},
  pages = {56-79},
  year = {2017}
}

Monodromy of Torus Fibrations and Decomposability Problem

Mahir Bilen Can and M. Topkara

Topology and Its Applications, 2017

Bib

@article{can2017monodromy,
  author = {Can, Mahir Bilen and Topkara, M.},
  title = {Monodromy of Torus Fibrations and Decomposability Problem},
  journal = {Topology and Its Applications},
  volume = {222},
  pages = {165-176},
  year = {2017}
}

An Analogue of Springer Fibers in Certain Wonderful Compactifications

Mahir Bilen Can, R. Howe, and M. Joyce

Journal of Algebra and Its Applications, 2017

Bib

@article{can2017analogue,
  author = {Can, Mahir Bilen and Howe, R. and Joyce, M.},
  title = {An Analogue of Springer Fibers in Certain Wonderful Compactifications},
  journal = {Journal of Algebra and Its Applications},
  volume = {16},
  number = {9},
  year = {2017}
}

AiM
Corrigendum to “Generators of the Hecke Algebra of (S_2n, B_n)”

Mahir Bilen Can and Ş. Özden

Advances in Mathematics, 2017

Abs arXiv Bib

In citeAC12, among other things, we observed that the structure constants of the Hecke algebra of the Gel’fand pair (S_2n,B_n) are polynomials in n. It is brought to attention by Omar Tout that there is a missing argument in its proof. Here we provide the details of the missing argument by further analyzing various actions of the hyperoctahedral group.
@article{can2017corrigendum, author = {Can, Mahir Bilen and {\"O}zden, {\c S}.}, title = {Corrigendum to ``Generators of the Hecke Algebra of $(S_{2n}, B_n)$''}, journal = {Advances in Mathematics}, volume = {308}, pages = {1337-1339}, year = {2017}, }
arXiv
On the Cohomology Rings of Grassmann Varieties and Hilbert Schemes

Mahir Bilen Can and Jeff Remmel

arXiv preprint, 2017

Abs arXiv Bib

By using vector field techniques, we compute the ordinary and equivariant cohomology rings of Hilbert scheme of points in the projective plane in relation with that of a Grassmann variety.
@article{can2017cohomology, author = {Can, Mahir Bilen and Remmel, Jeff}, title = {On the Cohomology Rings of Grassmann Varieties and Hilbert Schemes}, journal = {arXiv preprint}, year = {2017}, }
arXiv
Complexity c Pairs in Simple Algebraic Groups

Mahir Bilen Can

arXiv preprint, 2017

Abs arXiv Bib

We call a pair of closed subgroups (G_1,G_2) from a connected reductive algebraic group G a it complexity c pair if the multiplication action of the pair on G is of complexity c. The main focus of this article is on the cases where G is simple and c is either 0 or 1. After showing that both of the subgroups G_1 and G_2 cannot be reductive subgroups unless c>1, we look for the cases where exactly one of the subgroups G_1 and G_2 is reductive. It turns out that there are only a few such pairs, and their classification involves the horospherical homogeneous spaces of small ranks. As a byproduct of the circle of ideas that we use for this development, we obtain the classification of the diagonal spherical actions of simple algebraic groups on the products of flag varieties with affine homogeneous spaces.
@article{can2017complexity, author = {Can, Mahir Bilen}, title = {Complexity $c$ Pairs in Simple Algebraic Groups}, journal = {arXiv preprint}, year = {2017}, }

Algebraic Groups: Structure and Actions

2017

Bib

@book{can2017algebraic,
  editor = {Can, Mahir Bilen},
  title = {Algebraic Groups: Structure and Actions},
  series = {Proceedings of Symposia in Pure Mathematics},
  volume = {94},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2017},
  isbn = {978-1-4704-2601-9}
}

2016

Toroidal Affine Nash Groups

Mahir Bilen Can

Journal of Lie Theory, 2016

Bib

@article{can2016toroidal,
  author = {Can, Mahir Bilen},
  title = {Toroidal Affine Nash Groups},
  journal = {Journal of Lie Theory},
  volume = {26},
  number = {4},
  pages = {1069-1077},
  year = {2016}
}

JCTA

Chains in Weak Order Posets Associated to Involutions

Mahir Bilen Can, M. Joyce, and B. Wyser

Journal of Combinatorial Theory, Series A, 2016

Bib

@article{can2016chains,
  author = {Can, Mahir Bilen and Joyce, M. and Wyser, B.},
  title = {Chains in Weak Order Posets Associated to Involutions},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {137},
  pages = {207-225},
  year = {2016}
}

arXiv
Combinatorial Models for the Variety of Complete Quadrics

Mahir Bilen Can, S. Banerjee, and Michael Joyce

arXiv preprint, 2016

Abs arXiv Bib

We develop several combinatorial models that are useful in the study of the SL_n-variety mathcalX of complete quadrics. Barred permutations parameterize the fixed points of the action of a maximal torus T of SL_n, while μ-involutions parameterize the orbits of a Borel subgroup of SL_n. Using these combinatorial objects, we characterize the T-stable curves and surfaces on mathcalX, compute the T-equivariant K-theory of mathcalX, and describe a Białynicki-Birula cell decomposition for mathcalX. Furthermore, we give a computational characterization of the Bruhat order on Borel orbits in mathcalX.
@article{can2016combinatorial, author = {Can, Mahir Bilen and Banerjee, S. and Joyce, Michael}, title = {Combinatorial Models for the Variety of Complete Quadrics}, journal = {arXiv preprint}, year = {2016}, }
arXiv
Equivariant K-Theory of Smooth Projective Spherical Varieties

Mahir Bilen Can and S. Banerjee

arXiv preprint, 2016

Abs arXiv Bib

We present a description of the equivariant K-theory of a smooth projective spherical variety. This provides an integral K-theory version of Brion’s calculation of equivariant Chow-cohomology of such varieties. We consider the equivariant K-theory of wonderful compactifications of minimal rank symmetric varieties. We obtain a formula for their structure constants in terms of certain lower dimensional Schubert classes. This generalizes results of Uma on equivariant compactifications of adjoint groups.
@article{can2016equivariant, author = {Can, Mahir Bilen and Banerjee, S.}, title = {Equivariant $K$-Theory of Smooth Projective Spherical Varieties}, journal = {arXiv preprint}, year = {2016}, }

2015

Lexicographic Shellability of the Bruhat-Chevalley Order on Fixed-Point-Free Involutions

Mahir Bilen Can, Y. Cherniavsky, and T. Twelbeck

Israel Journal of Mathematics, 2015

Bib

@article{can2015lexicographic,
  author = {Can, Mahir Bilen and Cherniavsky, Y. and Twelbeck, T.},
  title = {Lexicographic Shellability of the Bruhat-Chevalley Order on Fixed-Point-Free Involutions},
  journal = {Israel Journal of Mathematics},
  volume = {207},
  number = {1},
  pages = {281-299},
  year = {2015}
}

Divisors and Specializations of Lucas Polynomials

Mahir Bilen Can, T. Amdeberhan, and M. Jensen

Journal of Combinatorics, 2015

Bib

@article{can2015divisors,
  author = {Can, Mahir Bilen and Amdeberhan, T. and Jensen, M.},
  title = {Divisors and Specializations of Lucas Polynomials},
  journal = {Journal of Combinatorics},
  volume = {6},
  number = {1-2},
  pages = {69-89},
  year = {2015}
}

Omitting Parentheses from the Cyclic Notation

Mahir Bilen Can and Y. Cherniavsky

Mediterranean Journal of Mathematics, 2015

Bib

@article{can2015omitting,
  author = {Can, Mahir Bilen and Cherniavsky, Y.},
  title = {Omitting Parentheses from the Cyclic Notation},
  journal = {Mediterranean Journal of Mathematics},
  volume = {12},
  number = {4},
  pages = {1199-1214},
  year = {2015}
}

Some Plethystic Identities and Kostka-Foulkes Polynomials

Mahir Bilen Can

Ars Combinatoria, 2015

Bib

@article{can2015plethystic,
  author = {Can, Mahir Bilen},
  title = {Some Plethystic Identities and Kostka-Foulkes Polynomials},
  journal = {Ars Combinatoria},
  volume = {122},
  pages = {411-421},
  year = {2015}
}

2014

SL(2)-Regular Subvarieties of Complete Quadrics

Mahir Bilen Can and M. Joyce

In Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics, 2014

Bib

@incollection{can2014sl2,
  author = {Can, Mahir Bilen and Joyce, M.},
  title = {SL(2)-Regular Subvarieties of Complete Quadrics},
  booktitle = {Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics},
  series = {Fields Institute Communications},
  volume = {71},
  publisher = {Springer},
  year = {2014}
}

Bruhat Order on Partial Fixed Point Free Involutions

Mahir Bilen Can, Y. Cherniavsky, and T. Twelbeck

Electronic Journal of Combinatorics, 2014

Bib

@article{can2014bruhat,
  author = {Can, Mahir Bilen and Cherniavsky, Y. and Twelbeck, T.},
  title = {Bruhat Order on Partial Fixed Point Free Involutions},
  journal = {Electronic Journal of Combinatorics},
  volume = {21},
  number = {4},
  year = {2014}
}

Lexicographic Shellability of Partial Involutions

Mahir Bilen Can and T. Twelbeck

Discrete Mathematics, 2014

Bib

@article{can2014lexicographic,
  author = {Can, Mahir Bilen and Twelbeck, T.},
  title = {Lexicographic Shellability of Partial Involutions},
  journal = {Discrete Mathematics},
  volume = {335},
  pages = {66-80},
  year = {2014}
}

On Bruhat Posets Associated to Compositions

Mahir Bilen Can and Y. Cherniavsky

In DMTCS Proceedings, 26th International Conference on Formal Power Series and Algebraic Combinatorics, 2014

Bib

@inproceedings{can2014posets,
  author = {Can, Mahir Bilen and Cherniavsky, Y.},
  title = {On Bruhat Posets Associated to Compositions},
  booktitle = {DMTCS Proceedings, 26th International Conference on Formal Power Series and Algebraic Combinatorics},
  year = {2014}
}

Calculating Heegaard-Floer Homology by Counting Lattice Points in Tetrahedra

Mahir Bilen Can and Ç. Karakurt

Acta Mathematica Hungarica, 2014

Bib

@article{can2014calculating,
  author = {Can, Mahir Bilen and Karakurt, {\c C}.},
  title = {Calculating Heegaard-Floer Homology by Counting Lattice Points in Tetrahedra},
  journal = {Acta Mathematica Hungarica},
  volume = {144},
  number = {1},
  pages = {43-75},
  year = {2014}
}

Branching through G_2

Mahir Bilen Can and Roger Howe

In Proceedings of the Gökova Geometry-Topology Conference 2013, 2014

Bib

@inproceedings{can2014branching,
  author = {Can, Mahir Bilen and Howe, Roger},
  title = {Branching through $G_2$},
  booktitle = {Proceedings of the G{\"o}kova Geometry-Topology Conference 2013},
  publisher = {G{\"o}kova Geometry/Topology Conference (GGT)},
  pages = {41-75},
  year = {2014}
}

Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

2014

DOI Bib

@book{can2014algebraic,
  editor = {Can, Mahir Bilen and Li, Zhenheng and Steinberg, Benjamin and Wang, Qiang},
  title = {Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics},
  series = {Fields Institute Communications},
  volume = {71},
  publisher = {Springer},
  year = {2014},
  doi = {10.1007/978-1-4939-0938-4}
}

2013

Unipotent Invariant Matrices

Mahir Bilen Can, R. Howe, and M. Joyce

Linear Algebra and Its Applications, 2013

Bib

@article{can2013unipotent,
  author = {Can, Mahir Bilen and Howe, R. and Joyce, M.},
  title = {Unipotent Invariant Matrices},
  journal = {Linear Algebra and Its Applications},
  volume = {439},
  number = {1},
  pages = {196-210},
  year = {2013}
}

TAMS

Weak Order on Complete Quadrics

Mahir Bilen Can and M. Joyce

Transactions of the American Mathematical Society, 2013

Bib

@article{can2013weak,
  author = {Can, Mahir Bilen and Joyce, M.},
  title = {Weak Order on Complete Quadrics},
  journal = {Transactions of the American Mathematical Society},
  volume = {365},
  number = {12},
  pages = {6269-6282},
  year = {2013}
}

On the Bruhat-Chevalley Order on Fixed-Point-Free Involutions

Mahir Bilen Can, Y. Cherniavsky, and T. Twelbeck

In The Seventh European Conference on Combinatorics, Graph Theory and Applications, 2013

Bib

@inproceedings{can2013involutions,
  author = {Can, Mahir Bilen and Cherniavsky, Y. and Twelbeck, T.},
  title = {On the Bruhat-Chevalley Order on Fixed-Point-Free Involutions},
  booktitle = {The Seventh European Conference on Combinatorics, Graph Theory and Applications},
  series = {CRM Series},
  volume = {16},
  publisher = {Edizioni della Normale, Pisa},
  pages = {457-462},
  year = {2013}
}

2012

JCTA

Ordered Bell Numbers, Hermite Polynomials, Skew Young Tableaux and Borel Orbits

Mahir Bilen Can and M. Joyce

Journal of Combinatorial Theory, Series A, 2012

Bib

@article{can2012ordered,
  author = {Can, Mahir Bilen and Joyce, M.},
  title = {Ordered Bell Numbers, Hermite Polynomials, Skew Young Tableaux and Borel Orbits},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {119},
  number = {8},
  pages = {1798-1810},
  year = {2012}
}

Irreducible Representations of Semisimple Algebraic Groups and Supersolvable Lattices

Mahir Bilen Can

Journal of Algebra, 2012

Bib

@article{can2012irreducible,
  author = {Can, Mahir Bilen},
  title = {Irreducible Representations of Semisimple Algebraic Groups and Supersolvable Lattices},
  journal = {Journal of Algebra},
  volume = {351},
  number = {1},
  pages = {235-250},
  year = {2012}
}

The Bruhat-Chevalley Ordering on the Rook Monoid

Mahir Bilen Can and L. E. Renner

Turkish Journal of Mathematics, 2012

Bib

@article{can2012rook,
  author = {Can, Mahir Bilen and Renner, L. E.},
  title = {The Bruhat-Chevalley Ordering on the Rook Monoid},
  journal = {Turkish Journal of Mathematics},
  volume = {36},
  pages = {499-519},
  year = {2012}
}

PAMS

From Parking Functions to Gelfand Pairs

Mahir Bilen Can and K. Aker

Proceedings of the American Mathematical Society, 2012

Bib

@article{can2012parking,
  author = {Can, Mahir Bilen and Aker, K.},
  title = {From Parking Functions to Gelfand Pairs},
  journal = {Proceedings of the American Mathematical Society},
  volume = {140},
  pages = {1113-1124},
  year = {2012}
}

AiM

Generators of the Hecke Algebra of (S_2n, B_n)

Mahir Bilen Can and K. Aker

Advances in Mathematics, 2012

Bib

@article{can2012generators,
  author = {Can, Mahir Bilen and Aker, K.},
  title = {Generators of the Hecke Algebra of $(S_{2n}, B_n)$},
  journal = {Advances in Mathematics},
  volume = {231},
  number = {5},
  pages = {2465-2483},
  year = {2012}
}

2011

Partitions, Rooks, and Symmetric Functions in Noncommuting Variables

Mahir Bilen Can and B. Sagan

Electronic Journal of Combinatorics, 2011

Bib

@article{can2011partitions,
  author = {Can, Mahir Bilen and Sagan, B.},
  title = {Partitions, Rooks, and Symmetric Functions in Noncommuting Variables},
  journal = {Electronic Journal of Combinatorics},
  volume = {18},
  number = {2},
  pages = {Paper 3},
  year = {2011}
}

Broken Bracelets, Molien Series, Paraffin Wax and an Elliptic Curve of Conductor 48

Mahir Bilen Can, T. Amdeberhan, and V. Moll

SIAM Journal on Discrete Mathematics, 2011

Bib

@article{can2011broken,
  author = {Can, Mahir Bilen and Amdeberhan, T. and Moll, V.},
  title = {Broken Bracelets, Molien Series, Paraffin Wax and an Elliptic Curve of Conductor 48},
  journal = {SIAM Journal on Discrete Mathematics},
  volume = {25},
  number = {4},
  pages = {1843-1859},
  year = {2011}
}

2010

R-Polynomials of Finite Monoids of Lie Type

Mahir Bilen Can, K. Aker, and M. Taşkin

International Journal of Algebra and Computation, 2010

Bib

@article{can2010rpolynomials,
  author = {Can, Mahir Bilen and Aker, K. and Ta{\c s}kin, M.},
  title = {$R$-Polynomials of Finite Monoids of Lie Type},
  journal = {International Journal of Algebra and Computation},
  volume = {20},
  number = {6},
  pages = {793-805},
  year = {2010}
}

2008

H-Polynomials and Rook Polynomials

Mahir Bilen Can and L. E. Renner

International Journal of Algebra and Computation, 2008

Bib

@article{can2008hpolynomials,
  author = {Can, Mahir Bilen and Renner, L. E.},
  title = {$H$-Polynomials and Rook Polynomials},
  journal = {International Journal of Algebra and Computation},
  volume = {18},
  number = {5},
  pages = {935-949},
  year = {2008}
}

Nested Hilbert Schemes and the Nested q,t-Catalan Series

Mahir Bilen Can

In DMTCS Proceedings, 20th International Conference on Formal Power Series and Algebraic Combinatorics, 2008

Bib

@inproceedings{can2008nested,
  author = {Can, Mahir Bilen},
  title = {Nested Hilbert Schemes and the Nested $q,t$-Catalan Series},
  booktitle = {DMTCS Proceedings, 20th International Conference on Formal Power Series and Algebraic Combinatorics},
  year = {2008}
}

2006

JCTA

A Proof of the q,t-Square Conjecture

Mahir Bilen Can and N. Loehr

Journal of Combinatorial Theory, Series A, 2006

Bib

@article{can2006proof,
  author = {Can, Mahir Bilen and Loehr, N.},
  title = {A Proof of the $q,t$-Square Conjecture},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {113},
  number = {7},
  pages = {1419-1434},
  year = {2006}
}