{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:32:39Z","timestamp":1762507959957,"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 consider the two permutation statistics which count the distinct pairs obtained from the final two terms of occurrences of patterns $\\tau_1\\cdots\\tau_{m-2}m(m-1)$ and $\\tau_1\\cdots\\tau_{m-2}(m-1)m$ in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group.  As a special case we derive a one-to-one correspondence between permutations which avoid each of the patterns $\\tau_1\\cdots\\tau_{m-2}m(m-1)\\in{\\cal S}_m$ and those which avoid each of the patterns $\\tau_1\\cdots\\tau_{m-2}(m-1)m\\in{\\cal S}_m$. For $m=3$ this correspondence coincides with the bijection given by Simion and Schmidt in [Europ. J. Combin. 6 (1985), 383-406].<\/jats:p>","DOI":"10.37236\/1686","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:23:18Z","timestamp":1578709398000},"source":"Crossref","is-referenced-by-count":1,"title":["A Generalization of Simion-Schmidt's Bijection for Restricted  Permutations"],"prefix":"10.37236","volume":"9","author":[{"given":"Astrid","family":"Reifegerste","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,6,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i2r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i2r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:07:38Z","timestamp":1579324058000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i2r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6,18]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2002,10,31]]}},"URL":"https:\/\/doi.org\/10.37236\/1686","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,6,18]]},"article-number":"R14"}}