A. Higashitani

activity

20092023

most citedArithmetic aspects of symmetric edge polytopes

30 citations · 184 across the 67 of their papers we have counts for

collaborators

Showing 2018Show all

5 papers · 1 filter

math.CO2018

Universal conditions on $h^{*}$ -vectors of lattice simplices

Akihiro Higashitani

In this paper, we will prove that given a lattice simplex with its $h^{*}$ -polynomial $\sum_{i \geq 0} h_{i}^{*} t^{i}$ , if $h_{k + 1}^{*} = \dots = h_{2 k}^{*} = 0$ holds, then there exists a lattice s…

math.CO2018

Levelness of toric rings arising from order and chain polytopes

Takayuki Hibi, Akihiro Higashitani

Let $K [O (P)]$ denote the toric ring of the order polytope $O (P)$ of a finite partially ordered set $P$ and $K [C (P)]$ that of the chain polytope $\math…

math.CO2018★ 30 cited

Arithmetic aspects of symmetric edge polytopes

Akihiro Higashitani, Katharina Jochemko, Mateusz Michałek

We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gröbner ba…

math.CO2018★ 3 cited

Smooth centrally symmetric polytopes in dimension 3 are IDP

Matthias Beck, Christian Haase, Akihiro Higashitani +4

In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric $3$ -dimensional polytopes, by s…

math.CO2018

Permutations with small maximal $k$ -consecutive sums

Akihiro Higashitani, Kazuki Kurimoto

Let $n$ and $k$ be positive integers with $n > k$ . Given a permutation $(π_{1}, \dots, π_{n})$ of integers $1, \dots, n$ , we consider $k$ -consecutive sums of $π$ , i.e., $s_i:=\sum_{j=0}^{k…

Universal conditions on h∗-vectors of lattice simplices

Levelness of toric rings arising from order and chain polytopes

Arithmetic aspects of symmetric edge polytopes

Smooth centrally symmetric polytopes in dimension 3 are IDP

Permutations with small maximal k-consecutive sums

Universal conditions on $h^{*}$ -vectors of lattice simplices

Permutations with small maximal $k$ -consecutive sums