{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T16:37:13Z","timestamp":1772815033742,"version":"3.50.1"},"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 generalize the notion of graded posets to what we call sign-graded (labeled) posets. We prove that the $W$-polynomial of a sign-graded poset is symmetric and unimodal. This extends a recent result of Reiner and Welker who proved it for graded posets by associating a simplicial polytopal sphere to each graded poset. By proving that the $W$-polynomials of sign-graded posets has the right sign at $-1$, we are able to prove the Charney-Davis Conjecture for these spheres (whenever they are flag).<\/jats:p>","DOI":"10.37236\/1866","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:20:33Z","timestamp":1578702033000},"source":"Crossref","is-referenced-by-count":25,"title":["Sign-Graded Posets, Unimodality of  $W$-Polynomials and the Charney-Davis Conjecture"],"prefix":"10.37236","volume":"11","author":[{"given":"Petter","family":"Br\u00e4nd\u00e9n","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:52:44Z","timestamp":1579305164000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2r9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1866","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,11,22]]},"article-number":"R9"}}