10 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…
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 a…
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…
New kinds of block diagonal matching fields and toric degenerations of Grassmannians
Akihiro Higashitani, Nobukazu Kowaki
Block diagonal matching field has many previous works. In general, a coherent matching field induces a monomial order to Plücker algebra, and block diagonal matching fields are a k…
Binomial edge rings of complete bipartite graphs
Akihiro Higashitani
We introduce a new class of algebras arising from graphs, called binomial edge rings. Given a graph on vertices with edges, the binomial edge ring of is defined to…
Classification of generalized Alexander quandles
Akihiro Higashitani, Seiichi Kamada, Jin Kosaka +1
The aim of this paper is to provide a new characterization of isomorphism classes of generalized Alexander quandles in terms of the underlying groups and their automorphisms. This…
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…
-vectors of edge rings of odd-cycle compositions
Kieran Bhaskara, Akihiro Higashitani, Nayana Shibu Deepthi
Let be the edge ring of a finite simple graph . Investigating properties of the -vector of is of great interest in combinatorial commutative a…