Akiyoshi Tsuchiya

Facets and volume of Gorenstein Fano polytopes

It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. It is then reasonable to ask whether every normal polytope is unimodularly equivalent to a face of some normal Gorenstein Fano polytope. In the present paper, it is shown that, by giving new classes of normal Gorenstein Fano polytopes, each order polytope as well as each chain polytope of dimension

Reflexive polytopes arising from perfect graphs

d

Edge rings with 3-linear resolutions

is unimodularly equivalent to a facet of some normal Gorenstein Fano polytopes of dimension

Reflexive polytopes arising from partially ordered sets and perfect graphs

d + 1

NONINCREASING DEPTH FUNCTIONS OF MONOMIAL IDEALS

. Furthermore, investigation on combinatorial properties, especially, Ehrhart polynomials and volume of these new polytopes will be achieved. Finally, some curious examples of Gorenstein Fano polytopes will be discovered.

Volume, Facets and Dual Polytopes of Twinned Chain Polytopes

Abstract Reflexive polytopes form one of the distinguished classes of lattice polytopes. Especially reflexive polytopes which possess the integer decomposition property are of interest. In the present paper, by virtue of the algebraic technique on Gronbner bases, a new class of reflexive polytopes which possess the integer decomposition property and which arise from perfect graphs will be presented. Furthermore, the Ehrhart δ-polynomials of these polytopes will be studied.

Self Dual Reflexive Simplices with Eulerian Polynomials

It is shown that the edge ring of a finite connected simple graph with a

Best possible lower bounds on the coefficients of Ehrhart polynomials

3

The ź -vectors of reflexive polytopes and of the dual polytopes

-linear resolution is a hypersurface.

Reflexive polytopes arising from edge polytopes

Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming from the order polytopes and the chain polytopes of finite partially ordered sets are known. In the present paper, we will generalize this result. In fact, by virtue of the algebraic technique on Gröbner bases, new classes of reflexive polytopes with the integer decomposition property coming from the order polytopes of finite partially ordered sets and the stable set polytopes of perfect graphs will be introduced. Furthermore, the result will give a polyhedral characterization of perfect graphs. Finally, we will investigate the Ehrhart