{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:06:22Z","timestamp":1763535982953,"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 study the generating function of descent numbers for the permutations with descent pairs of prescribed parities, the distribution of which turns out to be a refinement of median Genocchi numbers. We prove the $\\gamma$-positivity for the polynomial and derive the generating function for the $\\gamma$-vectors, expressed in the form of continued fraction. We also come up with an artificial statistic that gives a $q$-analogue of the $\\gamma$-positivity for the permutations with descents only allowed from an odd value to an odd value.<\/jats:p>","DOI":"10.37236\/10312","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T15:32:15Z","timestamp":1650555135000},"source":"Crossref","is-referenced-by-count":1,"title":["Gamma-Positivity for a Refinement of Median Genocchi Numbers"],"prefix":"10.37236","volume":"29","author":[{"given":"Sen-Peng","family":"Eu","sequence":"first","affiliation":[]},{"given":"Tung-Shan","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Hsin-Hao","family":"Lai","sequence":"additional","affiliation":[]},{"given":"Yuan-Hsun","family":"Lo","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,4,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T15:32:15Z","timestamp":1650555135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i2p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10312","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,4,22]]},"article-number":"P2.15"}}