{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,7]],"date-time":"2025-12-07T03:50:01Z","timestamp":1765079401914,"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 the problem of counting alternating permutations avoiding collections of permutation patterns including $132$.  We construct a bijection between the set $S_n(132)$ of $132$-avoiding permutations and the set $A_{2n + 1}(132)$ of alternating, $132$-avoiding permutations.  For every set $p_1, \\ldots, p_k$ of patterns and certain related patterns $q_1, \\ldots, q_k$, our bijection restricts to a bijection between $S_n(132, p_1, \\ldots, p_k)$, the set of permutations avoiding $132$ and the $p_i$, and $A_{2n + 1}(132, q_1, \\ldots, q_k)$, the set of alternating permutations avoiding $132$ and the $q_i$.  This reduces the enumeration of the latter set to that of the former.<\/jats:p>","DOI":"10.37236\/245","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:33:19Z","timestamp":1578717199000},"source":"Crossref","is-referenced-by-count":6,"title":["Alternating, Pattern-Avoiding Permutations"],"prefix":"10.37236","volume":"16","author":[{"given":"Joel Brewster","family":"Lewis","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:12:11Z","timestamp":1579317131000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/245","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,2,27]]},"article-number":"N7"}}