Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Matherne, Jacob P"'
We study the equivariant cohomology classes of torus-equivariant subvarieties of the space of matrices. For a large class of torus actions, we prove that the polynomials representing these classes (up to suitably changing signs) are covolume polynomi
Externí odkaz:
http://arxiv.org/abs/2411.17572
Three decades ago, Stanley and Brenti initiated the study of the Kazhdan--Lusztig--Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In the presen
Externí odkaz:
http://arxiv.org/abs/2411.04070
We study equivariant Kazhdan--Lusztig (KL) and $Z$-polynomials of matroids. We formulate an equivariant generalization of a result by Braden and Vysogorets that relates the equivariant KL and $Z$-polynomials of a matroid with those of a single-elemen
Externí odkaz:
http://arxiv.org/abs/2406.19962
Publikováno v:
Advances in Mathematics, Volume 449, July 2024, no. 109733
We study the Hilbert series of four objects arising in the Chow-theoretic and Kazhdan-Lusztig framework of matroids. These are, respectively, the Hilbert series of the Chow ring, the augmented Chow ring, the intersection cohomology module, and its st
Externí odkaz:
http://arxiv.org/abs/2212.03190
Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley--Stembridge conjecture, we
Externí odkaz:
http://arxiv.org/abs/2201.07333
Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the generalize
Externí odkaz:
http://arxiv.org/abs/2108.12927
Publikováno v:
Adv. Math. 408B (2022) 108596
The classical additive Deligne-Simpson problem is the existence problem for Fuchsian connections with residues at the singular points in specified adjoint orbits. Crawley-Boevey found the solution in 2003 by reinterpreting the problem in terms of qui
Externí odkaz:
http://arxiv.org/abs/2108.11029
Generalized splines are an algebraic combinatorial framework that generalizes and unifies various established concepts across different fields, most notably the classical notion of splines and the topological notion of GKM theory. The former consists
Externí odkaz:
http://arxiv.org/abs/2108.02757
Publikováno v:
In Advances in Mathematics July 2024 449
We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case
Externí odkaz:
http://arxiv.org/abs/2104.00715