{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:11:04Z","timestamp":1758823864302,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A polynomial $A(q)=\\sum_{i=0}^n a_iq^i$ is said to be unimodal if $a_0\\leqslant a_1\\leqslant \\cdots \\leqslant a_k\\geqslant a_{k+1} \\geqslant \\cdots \\geqslant a_n$. We investigate the unimodality of rational $q$-Catalan polynomials, which is defined to be $C_{m,n}(q)= \\frac{1}{[n+m]} {m+n \\brack n}_q $ for a coprime pair of positive integers $(m,n)$. We conjecture that they are unimodal with respect to parity, or equivalently, $(1+q)C_{m+n}(q)$ is unimodal. By using generating functions and the constant term method, we verify our our conjecture for $m\\le 5$ in a straightforward way.<\/jats:p>","DOI":"10.37236\/8870","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T05:50:50Z","timestamp":1578635450000},"source":"Crossref","is-referenced-by-count":3,"title":["On Parity Unimodality of $q$-Catalan Polynomials"],"prefix":"10.37236","volume":"27","author":[{"given":"Guoce","family":"Xin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yueming","family":"Zhong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,1,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p3\/7988","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p3\/7988","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T03:59:09Z","timestamp":1579233549000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8870","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,10]]},"article-number":"P1.3"}}