{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:22Z","timestamp":1753893802128,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Bisztriczky introduced the multiplex as a generalization of the simplex. A polytope is multiplicial if all its faces are multiplexes. In this paper it is proved that the flag vectors of multiplicial polytopes depend only on their face vectors.  A special class of multiplicial polytopes, also discovered by Bisztriczky, is comprised of the ordinary polytopes.  These are a natural generalization of the cyclic polytopes. The flag vectors of ordinary polytopes are determined.  This is used to give a surprisingly simple formula for the $h$-vector of the ordinary $d$-polytope with $n+1$ vertices and characteristic $k$: $h_i={k-d+i\\choose i}+(n-k){k-d+i-1\\choose i-1}$, for $i\\le d\/2$. In addition, a construction is given for 4-dimensional multiplicial polytopes having two-thirds of their vertices on a single facet, answering a question of Bisztriczky.<\/jats:p>","DOI":"10.37236\/1818","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:32:01Z","timestamp":1578691921000},"source":"Crossref","is-referenced-by-count":2,"title":["Flag Vectors of Multiplicial Polytopes"],"prefix":"10.37236","volume":"11","author":[{"given":"Margaret M.","family":"Bayer","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,9,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r65\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r65\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:53:56Z","timestamp":1579305236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r65"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1818","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,9,20]]},"article-number":"R65"}}