3 citations · 3 across the 1 of their papers we have counts for
10 papers
Odd cycles and Hilbert functions of their toric rings
Takayuki Hibi, Akiyoshi Tsuchiya
Studying Hilbert functions of concrete examples of normal toric rings, it is demonstrated that, for each , an -sequence $(h_0, h_1, \ldots, h_{2s-1}) \in \mathb…
Nef-partitions arising from unimodular configurations
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef-partition of a reflexive polytope is a decom…
Depth of an initial ideal
Takayuki Hibi, Akiyoshi Tsuchiya
Given an arbitrary integer , we construct a homogeneous ideal of the polynomial ring in variables over a filed for which is a C…
Enriched chain polytopes
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Stanley introduced a lattice polytope arising from a finite poset , which is called the chain polytope of . The geometric structure of has goo…
Reflexive polytopes arising from bipartite graphs with -positivity associated to interior polynomials
Hidefumi Ohsugi, Akiyoshi Tsuchiya
In this paper, we introduce polytopes arising from root systems and finite graphs , and study their combinatorial and algebraic properties. In particular,…
Stanley's non-Ehrhart-positive order polytopes
Fu Liu, Akiyoshi Tsuchiya
We say a polytope is Ehrhart positive if all the coefficients in its Ehrhart polynomial are positive. Answering an Ehrhart positivity question posed on Mathoverflow, Stanley provid…