41 citations · 122 across the 28 of their papers we have counts for
11 papers · 1 filter
Anisotropy and the -theorem for simplicial spheres
Eric Katz
We give an exposition of the proof of the lower bound part of the -theorem for simplicial spheres by Adiprasito, Papadakis, and Petrotou.
Volume Polynomials and Log-concavity of the Characteristic Polynomials of Matroids
Eric Katz
The Rota--Heron--Welsh conjecture (now a theorem of Adiprasito, Huh, and the author) asserts the log-concavity of the characteristic polynomial of matroids. We give an exposition o…
Matroidal Mixed Eulerian Numbers
Eric Katz, Max Kutler
We make a systematic study of matroidal mixed Eulerian numbers which are certain intersection numbers in the matroid Chow ring generalizing the mixed Eulerian numbers introduced by…
Poset subdivisions and the mixed cd-index
Patrick Dornian, Eric Katz, Ling Hei Tsang
The cd-index is an invariant of Eulerian posets expressed as a polynomial in noncommuting variables c and d. It determines another invariant, the h-polynomial. In this paper, we st…
Multivariate polynomials for generalized permutohedra
Eric Katz, McCabe Olsen
Using the notion of Mahonian statistic on acyclic posets, we introduce a -analogue of the -polynomial of a simple generalized permutohedron. We focus primarily on the case of…
Combinatorial Iterated Integrals and the Harmonic Volume of Graphs
Raymond Cheng, Eric Katz
Let be a connected bridgeless metric graph, and fix a point of . We define combinatorial iterated integrals on along closed paths at , a unipotent generalization…