{"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":1753893835115,"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 permutation $\\pi$ is said to avoid the permutation $\\tau$ if no subsequence in $\\pi$ has the same order relations as $\\tau$.  Two sets of permutations $\\Pi_1$ and $\\Pi_2$ are Wilf-equivalent if, for all $n$, the number of permutations of length $n$ avoiding all of the permutations in $\\Pi_1$ equals the number of permutations of length $n$ avoiding all of the permutations in $\\Pi_2$.  Using generating trees, we complete the problem of finding all Wilf-equivalences among pairs of permutations of which one has length 3 and the other has length 5 by proving that $\\{123,32541\\}$ is Wilf-equivalent to $\\{123,43251\\}$ and that $\\{123,42513\\}$ is Wilf-equivalent to $\\{132, 34215\\}$.  In addition, we provide generating trees for fourteen other pairs, among which there are two examples of pairs that give rise to isomorphic generating trees.<\/jats:p>","DOI":"10.37236\/1057","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:02:53Z","timestamp":1578718973000},"source":"Crossref","is-referenced-by-count":0,"title":["Completion of the Wilf-Classification of 3-5 Pairs Using Generating Trees"],"prefix":"10.37236","volume":"13","author":[{"given":"Mark","family":"Lipson","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,4,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:17:39Z","timestamp":1579321059000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4,4]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1057","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,4,4]]},"article-number":"R31"}}