{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:38Z","timestamp":1753893818076,"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 study questions of even-Wilf-equivalence, the analogue of Wilf-equivalence when attention is restricted to pattern avoidance by permutations in the alternating group.  Although some Wilf-equivalence results break when considering even-Wilf-equivalence analogues, we prove that other Wilf-equivalence results continue to hold in the even-Wilf-equivalence setting.  In particular, we prove that $t(t-1)\\cdots 321$ and $(t-1)(t-2)\\cdots 21t$ are even-shape-Wilf-equivalent for odd $t$, paralleling a result (which held for all $t$) of Backelin, West, and Xin for shape-Wilf-equivalence.  This allows us to classify the symmetric group $\\mathcal{S}_{4}$, and to partially classify $\\mathcal{S}_{5}$ and $\\mathcal{S}_{6}$, according to even-Wilf-equivalence.  As with transition to involution-Wilf-equivalence, some\u2014but not all\u2014of the classical Wilf-equivalence results are preserved when we make the transition to even-Wilf-equivalence.<\/jats:p>","DOI":"10.37236\/2024","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:36:32Z","timestamp":1578713792000},"source":"Crossref","is-referenced-by-count":1,"title":["Pattern Avoidance by Even Permutations"],"prefix":"10.37236","volume":"18","author":[{"given":"Andrew","family":"Baxter","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aaron D.","family":"Jaggard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,12,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:58:06Z","timestamp":1579301886000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i2p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,19]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/2024","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,12,19]]},"article-number":"P28"}}