{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T18:09:05Z","timestamp":1773943745300,"version":"3.50.1"},"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>In this paper, we define the $1\/k$-Eulerian polynomials of type $B$. Properties of these polynomials, including combinatorial interpretations, recurrence relations and $\\gamma$-positivity are studied. In particular, we show that the $1\/k$-Eulerian polynomials of type $B$ are $\\gamma$-positive when $k&gt;0$. Moreover, we define the $1\/k$-derangement polynomials of type $B$, denoted $d_n^B(x;k)$. We show that the polynomials $d_n^B(x;k)$ are bi-$\\gamma$-positive when $k\\geq 1\/2$. In particular, we get a symmetric decomposition of the polynomials $d_n^B(x;1\/2)$ in terms of the classical derangement polynomials.<\/jats:p>","DOI":"10.37236\/9313","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:01Z","timestamp":1599187681000},"source":"Crossref","is-referenced-by-count":1,"title":["The $1\/k$-Eulerian Polynomials of Type $B$"],"prefix":"10.37236","volume":"27","author":[{"given":"Shi-Mei","family":"Ma","sequence":"first","affiliation":[]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Jean","family":"Yeh","sequence":"additional","affiliation":[]},{"given":"Yeong-Nan","family":"Yeh","sequence":"additional","affiliation":[]}],"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\/v27i3p27\/8145","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p27\/8145","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:01Z","timestamp":1599187681000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p27"}},"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\/9313","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,7]]},"article-number":"P3.27"}}