{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:25Z","timestamp":1759335925016,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We identify several subsets of the partitions of $[n]$, each characterized by the avoidance of a pair of patterns, respectively of lengths four and five.\u00a0 Each of the classes we consider is enumerated by the Catalan numbers.\u00a0 Furthermore, the members of each class having a prescribed number of blocks are enumerated by the Narayana numbers.\u00a0 We use both algebraic and combinatorial methods to establish our results.\u00a0 In some of the cases, we make use of the kernel method to solve the recurrence arising when a further statistic is considered.\u00a0 In other cases, we define bijections with previously enumerated classes which preserve the number of blocks.\u00a0 Two of our bijections are of an algorithmic nature and systematically replace the occurrences of one pattern with those of another having the same length.<\/jats:p>","DOI":"10.37236\/2048","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:36:18Z","timestamp":1578713778000},"source":"Crossref","is-referenced-by-count":2,"title":["Pattern-Avoiding Set Partitions and Catalan Numbers"],"prefix":"10.37236","volume":"18","author":[{"given":"Toufik","family":"Mansour","sequence":"first","affiliation":[]},{"given":"Mark","family":"Shattuck","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,2,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:41:56Z","timestamp":1579300916000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i2p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,23]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/2048","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,2,23]]},"article-number":"P34"}}