{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:27Z","timestamp":1753893807087,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.37236\/1891","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:17:41Z","timestamp":1578719861000},"source":"Crossref","is-referenced-by-count":2,"title":["The $h$-Vector of a Gorenstein Toric Ring of a Compressed Polytope"],"prefix":"10.37236","volume":"11","author":[{"given":"Hidefumi","family":"Ohsugi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takayuki","family":"Hibi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,10,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2n4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2n4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:40Z","timestamp":1579322440000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2n4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1891","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,10,1]]},"article-number":"N4"}}