18 citations · 176 across the 52 of their papers we have counts for
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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,…
Integer decomposition property for Cayley sums of order and stable set polytopes
Takayuki Hibi, Hidefumi Ohsugi, Akiyoshi Tsuchiya
Lattice polytopes which possess the integer decomposition property (IDP for short) turn up in many fields of mathematics. It is known that if the Cayley sum of lattice polytopes po…
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…
Levelness of Order Polytopes
Christian Haase, Florian Kohl, Akiyoshi Tsuchiya
Since their introduction by Stanley~\cite{StanleyOrderPoly} order polytopes have been intriguing mathematicians as their geometry can be used to examine (algebraic) properties of f…
The depth of a reflexive polytope
Takayuki Hibi, Akiyoshi Tsuchiya
Given arbitrary integers and with and , a reflexive polytope of dimension with ${\rm depth} K[\mathca…
Cayley sums and Minkowski sums of lattice polytopes
Akiyoshi Tsuchiya
In this paper, we discuss the integer decomposition property for Cayley sums and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley sums have the integer dec…