{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852979,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For any $n &gt; 0$ and $0 \\leq m &lt; n$, let $P_{n,m}$ be the poset of projective equivalence classes of $\\{-,0,+\\}$-vectors of length $n$ with sign variation bounded by $m$, ordered by reverse inclusion of the positions of zeros. Let $\\Delta_{n,m}$ be the order complex of $P_{n,m}$. A previous result from the third author shows that $\\Delta_{n,m}$ is Cohen-Macaulay over $\\mathbb{Q}$ whenever $m$ is even or $m = n-1$. Hence, it follows that the $h$-vector of $\\Delta_{n,m}$ consists of nonnegative entries. Our main result states that $\\Delta_{n,m}$ is partitionable and we give an interpretation of the $h$-vector when\u00a0 $m$ is even or $m = n-1$. When $m = n-1$ the entries of the $h$-vector turn out to be the new Eulerian numbers of type $D$ studied by Borowiec and M\u0142otkowski in [\u00a0Electron. J. Combin., 23(1):#P1.38, 2016]. We then combine our main result with Klee's generalized Dehn-Sommerville relations to give a geometric proof of some facts about these Eulerian numbers of type $D$.<\/jats:p>","DOI":"10.37236\/9801","type":"journal-article","created":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T01:44:23Z","timestamp":1608774263000},"source":"Crossref","is-referenced-by-count":0,"title":["Sign Variation and Descents"],"prefix":"10.37236","volume":"27","author":[{"given":"Nantel","family":"Bergeron","sequence":"first","affiliation":[]},{"given":"Aram","family":"Dermenjian","sequence":"additional","affiliation":[]},{"given":"John","family":"Machacek","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,12,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p50\/8231","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p50\/8231","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T01:44:23Z","timestamp":1608774263000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,24]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9801","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,12,24]]},"article-number":"P4.50"}}