{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:28Z","timestamp":1753893808961,"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>Inspired by work of McKay, Morse, and Wilf, we give an exact count of the involutions in ${\\cal S}_{n}$ which contain a given permutation $\\tau\\in{\\cal S}_{k}$ as a subsequence; this number depends on the patterns of the first $j$ values of $\\tau$ for $1\\leq j\\leq k$. We then use this to define a partition of ${\\cal S}_{k}$, analogous to Wilf-classes in the study of pattern avoidance, and examine properties of this equivalence.  In the process, we show that a permutation $\\tau_1\\ldots\\tau_k$ is layered iff, for $1\\leq j\\leq k$, the pattern of $\\tau_1\\ldots\\tau_j$ is an involution.  We also obtain a result of Sagan and Stanley counting the standard Young tableaux of size $n$ which contain a fixed tableau of size $k$ as a subtableau.<\/jats:p>","DOI":"10.37236\/1911","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:19:00Z","timestamp":1578701940000},"source":"Crossref","is-referenced-by-count":2,"title":["Subsequence Containment by Involutions"],"prefix":"10.37236","volume":"12","author":[{"given":"Aaron D.","family":"Jaggard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,3,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:50:53Z","timestamp":1579305053000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1911","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,3,14]]},"article-number":"R14"}}