{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:33:56Z","timestamp":1759638836841,"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>The popularity of a pattern $p$ is the total number of copies of $p$ within all permutations of a set. We address popularity in the set of $132$-avoidng permutations. B\u00f3na showed that in this set, all other non-monotone length-$3$ patterns are equipopular, and proved equipopularity relations between some length-$k$ patterns of a specific form. We prove equipopularity relations between general length-$k$ patterns, based on the structure of their corresponding binary plane trees. Our result explains all equipopularity relations for patterns of length up to $7$, and we conjecture that it provides a complete classification of equipopularity in $132$-avoiding permutations.<\/jats:p>","DOI":"10.37236\/2634","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:00:42Z","timestamp":1578693642000},"source":"Crossref","is-referenced-by-count":5,"title":["Pattern Popularity in 132-Avoiding Permutations"],"prefix":"10.37236","volume":"20","author":[{"given":"Kate","family":"Rudolph","sequence":"first","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\/v20i1p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:20:30Z","timestamp":1579281630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p8"}},"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\/2634","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,1,14]]},"article-number":"P8"}}