{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:20:22Z","timestamp":1759335622632,"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>Conditions are given on a lattice polytope $P$ of dimension $m$ or its  associated affine semigroup ring which imply inequalities for the  $h^*$-vector $(h^*_0, h^*_1,\\dots,h^*_m)$ of $P$ of the form $h^*_i \\ge  h^*_{d-i}$ for $1 \\le i \\le \\lfloor d \/ 2 \\rfloor$ and $h^*_{\\lfloor d \/ 2  \\rfloor} \\ge h^*_{\\lfloor d \/ 2 \\rfloor + 1} \\ge \\cdots \\ge h^*_d$, where  $h^*_i = 0$ for $d  &lt;  i \\le m$. Two applications to order polytopes of  posets and stable polytopes of perfect graphs are included. <\/jats:p>","DOI":"10.37236\/1863","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:20:41Z","timestamp":1578720041000},"source":"Crossref","is-referenced-by-count":25,"title":["$h^*$-Vectors, Eulerian Polynomials and Stable Polytopes of Graphs"],"prefix":"10.37236","volume":"11","author":[{"given":"Christos A.","family":"Athanasiadis","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,10,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:53:26Z","timestamp":1579323206000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2r6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,7]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1863","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,10,7]]},"article-number":"R6"}}