14 citations · 44 across the 19 of their papers we have counts for
26 papers
The parity module of a matroid
Tom Braden, June Huh, Jacob P. Matherne +2
We introduce the parity module of a matroid with coefficients in a field . When has characteristic zero, we show that the parity module of a matroid is iso…
Chromatic symmetric functions of claw-free graphs are not Schur positive
Jacob P. Matherne, Alejandro H. Morales
Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize chromatic polynomials of graphs. In 1995, Stanley introduced these sym…
Universality theorems for generalized splines
Jacob Matherne, Eric Ramos, Julianna Tymoczko
We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, whi…
Inverse Kazhdan-Lusztig polynomials of matroids under deletion
Tom Braden, Luis Ferroni, Jacob P. Matherne +1
We provide a deletion formula for the inverse Kazhdan--Lusztig polynomial and the inverse -polynomial of a matroid. Our formulas provide analogues to the deletion formulas of Br…
Syzygies of polymatroidal ideals
Yairon Cid-Ruiz, Jacob P. Matherne, Anna Shapiro
We introduce the cave polynomial of a polymatroid and show that it yields a valuative function on polymatroids. The support of this polynomial after homogenization is again a polym…
Building sets, Chow rings, and their Hilbert series
Christopher Eur, Luis Ferroni, Jacob P. Matherne +2
We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new…
Log-concavity of characters of parabolic Verma modules, and of restricted Kostant partition functions
Apoorva Khare, Jacob P. Matherne, Avery St. Dizier
In 2022, Huh-Matherne-Mészáros-St. Dizier showed that normalized Schur polynomials are Lorentzian, thereby yielding their continuous (resp. discrete) log-concavity on the positive…
Log-concavity of polynomials arising from equivariant cohomology
Yairon Cid-Ruiz, Yupeng Li, Jacob P. Matherne
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 representi…
Chow functions for partially ordered sets
Luis Ferroni, Jacob P. Matherne, Lorenzo Vecchi
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 comb…
Deletion formulas for equivariant Kazhdan-Lusztig polynomials of matroids
Luis Ferroni, Jacob P. Matherne, Lorenzo Vecchi
We study equivariant Kazhdan--Lusztig (KL) and -polynomials of matroids. We formulate an equivariant generalization of a result by Braden and Vysogorets that relates the equivar…
Hilbert-Poincaré series of matroid Chow rings and intersection cohomology
Luis Ferroni, Jacob P. Matherne, Matthew Stevens +1
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, t…
The Newton polytope and Lorentzian property of chromatic symmetric functions
Jacob P. Matherne, Alejandro H. Morales, Jesse Selover
Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and d…
A continuous associahedron of type A
Maitreyee C. Kulkarni, Jacob P. Matherne, Kaveh Mousavand +1
Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show…
The Deligne-Simpson problem for connections on with a maximally ramified singularity
Maitreyee C. Kulkarni, Neal Livesay, Jacob P. Matherne +2
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 fo…
Generalized splines on graphs with two labels and polynomial splines on cycles
Portia Anderson, Jacob P. Matherne, Julianna Tymoczko
Generalized splines are an algebraic combinatorial framework that generalizes and unifies various established concepts across different fields, most notably the classical notion of…
Equivariant log concavity and representation stability
Jacob P. Matherne, Dane Miyata, Nicholas Proudfoot +1
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 matroi…
Singular Hodge theory for combinatorial geometries
Tom Braden, June Huh, Jacob P. Matherne +2
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. As applicati…
Counting linear extensions of posets with determinants of hook lengths
Alexander Garver, Stefan Grosser, Jacob P. Matherne +1
We introduce a class of posets, which includes both ribbon posets (skew shapes) and -complete posets, such that their number of linear extensions is given by a determinant of a…
A semi-small decomposition of the Chow ring of a matroid
Tom Braden, June Huh, Jacob P. Matherne +2
We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem, and…
Logarithmic concavity of Schur and related polynomials
June Huh, Jacob P. Matherne, Karola Mészáros +1
We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the sp…
Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions
Eric Bucher, Chris Eppolito, Jaiung Jun +1
In this paper, we give a cancellation-free antipode formula for the matroid-minor Hopf algebra. We then explore applications of this formula. For example, the cancellation-free for…
Combinatorics of Fourier transforms for type A quiver representations
Pramod N. Achar, Maitreyee C. Kulkarni, Jacob P. Matherne
We describe two new combinatorial algorithms (using the language of "triangular arrays") for computing the Fourier transforms of simple perverse sheaves on the moduli space of repr…
A cancellation-free antipode formula (for uniform matroids) for the restriction-contraction matroid Hopf algebra
Eric Bucher, Jacob P. Matherne
In this paper, we give a cancellation-free antipode formula (for uniform matroids) for the restriction-contraction matroid Hopf algebra, using the technique of splitting and mergin…
Combinatorics of exceptional sequences in type A
Alexander Garver, Kiyoshi Igusa, Jacob P. Matherne +1
Exceptional sequences are certain ordered sequences of quiver representations. We introduce a class of objects called strand diagrams and use this model to classify exceptional seq…