{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834413,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Eulerian polynomial $A_n(t)$ enumerating descents in $\\mathfrak{S}_n$ is known to be gamma positive for all $n$. When enumeration is done over the type B and type D Coxeter groups, the type B and type D Eulerian polynomials are also known to be gamma\u00a0positive for all $n$.\r\nWe consider $A_n^+(t)$ and $A_n^-(t)$, the polynomials which enumerate descents in the alternating group $\\mathcal{A}_n$ and in\u00a0$\\mathfrak{S}_n - \\mathcal{A}_n$ respectively.\u00a0 We show the following results about $A_n^+(t)$ and $A_n^-(t)$: both polynomials are gamma positive iff $n \\equiv 0,1$ (mod 4). When $n \\equiv 2,3$ (mod 4), both polynomials are not palindromic. When $n \\equiv 2$ (mod 4), we show that {\\sl two} gamma positive summands add up to give $A_n^+(t)$ and $A_n^-(t)$. When $n \\equiv 3$ (mod 4), we show that {\\sl three} gamma positive summands add up to give both $A_n^+(t)$ and $A_n^-(t)$.\u00a0\r\nWe show similar gamma positivity results about the descent based type B and type D Eulerian polynomials when enumeration is done over the positive elements in the respective Coxeter groups. We also show that the polynomials considered in this work are unimodal.<\/jats:p>","DOI":"10.37236\/9037","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:08Z","timestamp":1599187688000},"source":"Crossref","is-referenced-by-count":3,"title":["Gamma Positivity of the Descent Based Eulerian Polynomial in Positive Elements of Classical Weyl Groups"],"prefix":"10.37236","volume":"27","author":[{"given":"Hiranya Kishore","family":"Dey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sivaramakrishnan","family":"Sivasubramanian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,8,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p20\/8138","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p20\/8138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:09Z","timestamp":1599187689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,7]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9037","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,8,7]]},"article-number":"P3.20"}}