Year: 2005
Type: article
Abstract: A compressed polytope is an integral convex polytope all of whose pulling triangulations are unimodular. A $(q - 1)$-simplex $\Sigma$ each of whose vertices is a vertex of a convex polytope ${\cal P}$ is said to be a special simplex in ${\cal P}$ if each facet of ${\cal P}$ contains exactly $q - 1$ of the vertices of $\Sigma$. It will be proved that there is a special simplex in a compressed polytope ${\cal P}$ if (and only if) its toric ring $K[{\cal P}]$ is Gorenstein. In consequence it follows that the $h$-vector of a Gorenstein toric ring $K[{\cal P}]$ is unimodal if ${\cal P}$ is compressed.
DOI: 10.37236/1891
Authors: Hidefumi Ohsugi, Takayuki Hibi
Institutions: Rikkyo University, The University of Osaka
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W1551862907