The \(h\)-vector of a Gorenstein toric ring of a compressed polytope
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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
Classification :
52B20, 13H10
Mots-clés : integral polytope, unimodular, compressed, \(h\)-vector, toric ring, Gorenstein
Mots-clés : integral polytope, unimodular, compressed, \(h\)-vector, toric ring, Gorenstein
@article{10_37236_1891,
author = {Hidefumi Ohsugi and Takayuki Hibi},
title = {The \(h\)-vector of a {Gorenstein} toric ring of a compressed polytope},
journal = {The electronic journal of combinatorics},
year = {2004},
volume = {11},
number = {2},
doi = {10.37236/1891},
zbl = {1085.52009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1891/}
}
Hidefumi Ohsugi; Takayuki Hibi. The \(h\)-vector of a Gorenstein toric ring of a compressed polytope. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1891
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