{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:00Z","timestamp":1753893780337,"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>Let $b(n,k)$ denote the number of permutations of $\\{1,\\ldots,n\\}$ with precisely $k$ inversions. We represent $b(n,k)$ as a real trigonometric integral and then use the method of Laplace to give a complete asymptotic expansion of the integral. Among the consequences, we have a complete asymptotic expansion for $b(n,k)\/n!$ for a range of $k$ including the maximum of the $b(n,k)\/n!$.<\/jats:p>","DOI":"10.37236\/1528","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:03:06Z","timestamp":1578690186000},"source":"Crossref","is-referenced-by-count":2,"title":["An Asymptotic Expansion for the Number of  Permutations with a Certain Number of Inversions"],"prefix":"10.37236","volume":"7","author":[{"given":"Lane","family":"Clark","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2000,8,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:22:23Z","timestamp":1579306943000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,8,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1528","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,8,8]]},"article-number":"R50"}}