{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T06:44:29Z","timestamp":1784270669665,"version":"3.55.0"},"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>Ehrenborg obtained asymptotic results for nearly alternating permutations and conjectured an asymptotic formula for the number of permutations that have a nearly periodic run pattern.  We prove a generalization of this conjecture, rederive the fact that the asymptotic number of permutations with a periodic run pattern has the form $Cr^{-n}\\,n!$, and show how to compute the various constants.  A reformulation in terms of iid random variables leads to an eigenvalue problem for a Fredholm integral equation.  Tools from functional analysis establish the necessary properties.<\/jats:p>","DOI":"10.37236\/1733","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:02:58Z","timestamp":1578639778000},"source":"Crossref","is-referenced-by-count":5,"title":["Asymptotics of Permutations with Nearly Periodic Patterns of Rises and Falls"],"prefix":"10.37236","volume":"10","author":[{"given":"Edward A.","family":"Bender","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William J.","family":"Helton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L. Bruce","family":"Richmond","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2003,10,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:06:29Z","timestamp":1579323989000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1733","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,10,23]]},"article-number":"R40"}}