18 citations · 176 across the 52 of their papers we have counts for
9 papers · 1 filter
Reflexive polytopes arising from edge polytopes
Takahiro Nagaoka, Akiyoshi Tsuchiya
It is known that every lattice polytope is unimodularly equivalent to a face of some reflexive polytope. A stronger question is to ask whether every -polytope is unimodularl…
Edge rings with -linear resolutions
Takayuki Hibi, Kazunori Matsuda, Akiyoshi Tsuchiya
It is shown that the edge ring of a finite connected simple graph with a -linear resolution is a hypersurface.
Laplacian Simplices Associated to Digraphs
Gabriele Balletti, Takayuki Hibi, Marie Meyer +1
We associate to a finite digraph a lattice polytope whose vertices are the rows of the Laplacian matrix of . This generalizes a construction introduced by Braun and th…
Ehrhart polynomials of lattice polytopes with normalized volumes
Akiyoshi Tsuchiya
A complete classification of the -vectors of lattice polytopes whose normalized volumes are at most is known. In the present paper, we will classify all the -vectors of l…
Classification of lattice polytopes with small volumes
Takayuki Hibi, Akiyoshi Tsuchiya
In the frame of a classification of general square systems of polynomial equations solvable by radicals, Esterov and Gusev succeeded in classifying all spanning lattice polytopes w…
Gorenstein simplices with a given -polynomial
Takayuki Hibi, Akiyoshi Tsuchiya, Koutarou Yoshida
To classify the lattice polytopes with a given -polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized…
Reflexive polytopes arising from partially ordered sets and perfect graphs
Takayuki Hibi, Akiyoshi Tsuchiya
Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming fr…
Reflexive polytopes arising from perfect graphs
Takayuki Hibi, Akiyoshi Tsuchiya
Reflexive polytopes form one of the distinguished classes of lattice polytopes. Especially reflexive polytopes which possess the integer decomposition property are of interest. In…
Gorenstein simplices and the associated finite abelian groups
Akiyoshi Tsuchiya
It is known that a lattice simplex of dimension corresponds a finite abelian subgroup of . Conversely, given a finite abelian subgroup of $(\math…