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 2012Show all

6 papers · 1 filter

math.GR2012

Distribution of accumulation points of roots for type $(n - 1, 1)$ Coxeter groups

Akihiro Higashitani, Ryosuke Mineyama, Norihiro Nakashima

In this paper, we investigate the set of accumulation points of normalized roots of infinite Coxeter groups for certain class of their action. Concretely, we prove the conjecture p…

math.CO2012

Integer decomposition property of dilated polytopes

David A. Cox, Christian Haase, Takayuki Hibi +1

Let $P \subset R^{N}$ be an integral convex polytope of dimension $d$ and write $k P$ , where $k = 1, 2, \dots$ , for dilations of $P$ . We say t…

math.CO2012

Non-normal very ample polytopes and their holes

Akihiro Higashitani

In this paper, we show that for given integers $h$ and $d$ with $h \geq 1$ and $d \geq 3$ , there exists a non-normal very ample integral convex polytope of dimension $d$ which has…

math.AC2012★ 2 cited

Toric rings arising from cyclic polytopes

Takayuki Hibi, Akihiro Higashitani, Lukas Katth"an +1

In the present paper, we consider the problem when the toric ring arising from an integral cyclic polytope is Cohen-Macaulay by discussing Serre's condition and we give a complete…

math.CO2012★ 8 cited

Lattice multi-polygons

Akihiro Higashitani, Mikiya Masuda

We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $Z^{2}$ .…

math.CO2012★ 5 cited

Normal cyclic polytopes and cyclic polytopes that are not very ample

Takayuki Hibi, Akihiro Higashitani, Lukas Katthän +1

Let $d$ and $n$ be positive integers with $n \geq d + 1$ and $τ_{1}, ..., τ_{n}$ integers with $τ_{1} < ... < τ_{n}$ . Let $C_{d}(τ_{1}, ..., τ_{n}) \subset \RR^{d}$ denote the cycl…