30 citations · 184 across the 67 of their papers we have counts for
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The root distributions of Ehrhart polynomials of free sums of reflexive polytopes
Masahiro Hachimori, Akihiro Higashitani, Yumi Yamada
In this paper, we study the root distributions of Ehrhart polynomials of free sums of certain reflexive polytopes. We investigate cases where the roots of the Ehrhart polynomials o…
Three families of toric rings arising from posets or graphs with small class groups
Akihiro Higashitani, Koji Matsushita
The main objects of the present paper are (i) Hibi rings (toric rings arising from order polytopes of posets), (ii) stable set rings (toric rings arising from stable set polytopes…
Combinatorial classification of -skew projective spaces
Akihiro Higashitani, Kenta Ueyama
The noncommutative projective scheme of a -skew polynomial algebra in variables is considered to be a -skew projecti…
Combinatorial mutations of Newton-Okounkov polytopes arising from plabic graphs
Akihiro Higashitani, Yusuke Nakajima
It is known that the homogeneous coordinate ring of a Grassmannian has a cluster structure, which is induced from the combinatorial structure of a plabic graph. A plabic graph is a…
Period collapse in characteristic quasi-polynomials of hyperplane arrangements
Akihiro Higashitani, Tan Nhat Tran, Masahiko Yoshinaga
Given an integral hyperplane arrangement, Kamiya-Takemura-Terao (2008 & 2011) introduced the notion of characteristic quasi-polynomial, which enumerates the cardinality of the comp…
The ratio of the numbers of odd and even cycles in outerplanar graphs
Akihiro Higashitani, Naoki Matsumoto
In this paper, we investigate the ratio of the numbers of odd and even cycles in outerplanar graphs. We verify that the ratio generally diverges to infinity as the order of a graph…