{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:15:41Z","timestamp":1758824141563,"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>We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's $3^d$ conjecture for such polytopes (they all have at least $3^d$ nonempty faces) and show that the Hanner polytopes among them (which have exactly $3^d$ nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only $3^d+16$ nonempty faces.<\/jats:p>","DOI":"10.37236\/3315","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:56:48Z","timestamp":1578707808000},"source":"Crossref","is-referenced-by-count":4,"title":["Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs"],"prefix":"10.37236","volume":"20","author":[{"given":"Ragnar","family":"Freij","sequence":"first","affiliation":[]},{"given":"Matthias","family":"Henze","sequence":"additional","affiliation":[]},{"given":"Moritz W.","family":"Schmitt","sequence":"additional","affiliation":[]},{"given":"G\u00fcnter M.","family":"Ziegler","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,5,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:20:31Z","timestamp":1579242031000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/3315","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,5,16]]},"article-number":"P32"}}