2 citations · 2 across the 3 of their papers we have counts for
12 papers
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…
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 applicat…
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…
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…
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 positiv…