9 papers
Minkowski decomposability of symmetric edge polytopes
Akihiro Higashitani, Aki Mori
In this paper, we study the Minkowski decomposability of symmetric edge polytopes of a finite simple graph on vertex set . More precisely, we give a complete cha…
A matroidal criterion for flow polytopes to be order polytopes
Akihiro Higashitani, Hidefumi Ohsugi
Flow polytopes of directed acyclic graphs form a central class of lattice polytopes in algebraic, geometric, and enumerative combinatorics. Order polytopes are one of the best unde…
Characterization and chromatic number of triangle-free graphs with diameter 2
Akihiro Higashitani, Diogo Kendy Matsumoto, Naoki Matsumoto
In this paper, we consider triangle-free graphs with diameter 2. If a triangle-free graph with diameter 2 is not isomorphic to a star, then the radius of is also 2, where s…
On the Ehrhart Theory of Generalized Symmetric Edge Polytopes
Robert Davis, Akihiro Higashitani, Hidefumi Ohsugi
The symmetric edge polytope (SEP) of a (finite, undirected) graph is a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. SEPs have been stu…
Fans and polytopes in tilting theory III: Classification of convex -fans of rank 3
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
The -fan of a finite dimensional algebra is a non-singular fan in its real Grothendieck group, defined by tilting theory. If the union of the simplices…
Order polytopes of graded posets are gamma-effective
Alessio D'Alì, Akihiro Higashitani
Order polytopes of posets have been a very rich topic at the crossroads between combinatorics and discrete geometry since their definition by Stanley in 1986. Among other notable r…