{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:30Z","timestamp":1759335930016,"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>Let $f_n^r(k)$ be the number of 132-avoiding permutations on $n$ letters that contain exactly $r$ occurrences of $12\\dots k$, and let $F_r(x;k)$ and $F(x,y;k)$ be the generating functions defined by $F_r(x;k)=\\sum_{n\\ge 0} f_n^r(k)x^n$ and $F(x,y;k)=\\sum_{r\\ge 0}F_r(x;k)y^r$. We find an explicit expression for $F(x,y;k)$ in the form of a continued fraction. This allows us to express $F_r(x;k)$ for $1\\le r\\le k$ via Chebyshev polynomials of the second kind.<\/jats:p>","DOI":"10.37236\/1495","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:05:19Z","timestamp":1578708319000},"source":"Crossref","is-referenced-by-count":23,"title":["Restricted permutations, continued fractions, and Chebyshev polynomials"],"prefix":"10.37236","volume":"7","author":[{"given":"Toufik","family":"Mansour","sequence":"first","affiliation":[]},{"given":"Alek","family":"Vainshtein","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:24:57Z","timestamp":1579325097000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1495","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,2,27]]},"article-number":"R17"}}