30 citations · 184 across the 67 of their papers we have counts for
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Examples and counterexamples in Ehrhart theory
Luis Ferroni, Akihiro Higashitani
This article provides a comprehensive exposition about inequalities that the coefficients of Ehrhart polynomials and -polynomials satisfy under various assumptions. We pay par…
Ehrhart quasi-polynomials and parallel translations
Akihiro Higashitani, Satoshi Murai, Masahiko Yoshinaga
Given a rational polytope , the numerical function counting lattice points in the integral dilations of is known to become a quasi-polynomial, called the…
Adjacency matrices over a finite prime field and their direct sum decompositions
Akihiro Higashitani, Yuya Sugishita
In this paper, we discuss the adjacency matrices of finite undirected simple graphs over a finite prime field . We apply symmetric (row and column) elementary transfo…
Restricted Chain-Order Polytopes via Combinatorial Mutations
Oliver Clarke, Akihiro Higashitani, Francesca Zaffalon
We study restricted chain-order polytopes associated to Young diagrams using combinatorial mutations. These polytopes are obtained by intersecting chain-order polytopes with certai…
The equivariant Ehrhart theory of polytopes with order-two symmetries
Oliver Clarke, Akihiro Higashitani, Max Kölbl
We study the equivariant Ehrhart theory of families of polytopes that are invariant under a non-trivial action of the group with order two. We study families of polytopes whose equ…
Combinatorial Mutations of Gelfand-Tsetlin Polytopes, Feigin-Fourier-Littelmann-Vinberg Polytopes, and Block Diagonal Matching Field Polytopes
Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
The Gelfand-Tsetlin and the Feigin-Fourier-Littelmann-Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bas…