{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835902,"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>We study q-analogues of k-Fibonacci numbers that arise from weighted tilings of an $n\\times1$ board with tiles of length at most k. \u00a0The weights on our tilings arise naturally out of distributions of permutations statistics and set partitions statistics. \u00a0We use these q-analogues to produce q-analogues of identities involving k-Fibonacci numbers. \u00a0This is a natural extension of results of the first author and Sagan on set partitions and the first author and Mathisen on permutations. \u00a0In this paper we give general q-analogues of k-Fibonacci identities for arbitrary weights that depend only on lengths and locations of tiles. \u00a0We then determine weights for specific permutation or set partition statistics and use these specific weights and the general identities to produce specific identities.<\/jats:p>","DOI":"10.37236\/2550","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:45Z","timestamp":1578711645000},"source":"Crossref","is-referenced-by-count":0,"title":["Statistical Distributions and $q$-Analogues of $k$-Fibonacci Numbers"],"prefix":"10.37236","volume":"20","author":[{"given":"Adam M","family":"Goyt","sequence":"first","affiliation":[]},{"given":"Brady L","family":"Keller","sequence":"additional","affiliation":[]},{"given":"Jonathan E","family":"Rue","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,1,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:20:32Z","timestamp":1579299632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2550","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,1,14]]},"article-number":"P7"}}