{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:22Z","timestamp":1753893862334,"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>Let $\\left[{n \\atop k}\\right]_q$ be a $q$-binomial coefficient. Stanley conjectured that the function $f_{k,R}(n) = \\left|\\left\\{\\alpha : [q^{\\alpha}] \\left[{n \\atop k}\\right]_q\u00a0 \\equiv R \\pmod{N}\\right\\}\\right|$ is quasi-polynomial for $N$ prime. We prove this for any integer $N$ and obtain an expression for the generating function $F_{k,R}(x)$ for $f_{k,R}(n)$.<\/jats:p>","DOI":"10.37236\/7820","type":"journal-article","created":{"date-parts":[[2020,6,26]],"date-time":"2020-06-26T00:52:04Z","timestamp":1593132724000},"source":"Crossref","is-referenced-by-count":0,"title":["Coefficients of Gaussian Polynomials Modulo $N$"],"prefix":"10.37236","volume":"27","author":[{"given":"Dylan","family":"Pentland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,6,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/V27i2p58\/8115","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/V27i2p58\/8115","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,26]],"date-time":"2020-06-26T00:52:19Z","timestamp":1593132739000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/V27i2p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/7820","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,6,17]]},"article-number":"P2.58"}}