30 citations · 184 across the 67 of their papers we have counts for
6 papers · 1 filter
An algebraic reduction of Hedetniemi's conjecture
Ryoya Fukasaku, Michitaka Furuya, Akihiro Higashitani
For a graph , let denote the chromatic number. In graph theory, the following famous conjecture posed by Hedetniemi has been studied: For two graphs and , $χ(G\tim…
Generalized F-signatures of Hibi rings
Akihiro Higashitani, Yusuke Nakajima
The -signature is a numerical invariant defined by the number of free direct summands in the Frobenius push-forward, and it measures singularities in positive characteristic. It…
Combinatorial study of stable categories of graded Cohen--Macaulay modules over skew quadric hypersurfaces
Akihiro Higashitani, Kenta Ueyama
In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let be a graded ()-skew polynomial algebra in…
Toric ideals of Minkowski sums of unit simplices
Akihiro Higashitani, Hidefumi Ohsugi
In this paper, we discuss the toric ideals of Minkowski sums of unit simplices. More precisely, we prove that the toric ideal of Minkowski sum of unit simplices has a squarefree in…
Deformations of Dimer Models
Akihiro Higashitani, Yusuke Nakajima
The combinatorial mutation of polygons, which transforms a given lattice polygon into another one, is an important operation to understand mirror partners for two-dimensional Fano…
Winding Number of -modular sequences and Applications to the Singularity Content of a Fano Polygon
Daniel Cavey, Akihiro Higashitani
By generalising the notion of a unimodular sequence, we create an expression for the winding number of certain ordered sets of lattice points. Since the winding number of the verti…