{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T04:39:32Z","timestamp":1790483972167,"version":"4.1.0"},"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>The probability that a random pair of elements from the alternating group $A_{n}$ generates all of $A_{n}$ is shown to have an asymptotic expansion of the form $1-1\/n-1\/n^{2}-4\/n^{3}-23\/n^{4}-171\/n^{5}-... $.  This same asymptotic expansion is valid for the probability that a random pair of elements from the symmetric group $S_{n}$ generates either $A_{n}$ or $S_{n}$. Similar results hold for the case of $r$ generators ($r&gt;2$).<\/jats:p>","DOI":"10.37236\/1953","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:09:03Z","timestamp":1578719343000},"source":"Crossref","is-referenced-by-count":13,"title":["Asymptotics of Generating the Symmetric and Alternating Groups"],"prefix":"10.37236","volume":"12","author":[{"given":"John D.","family":"Dixon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2005,11,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r56\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r56\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:14Z","timestamp":1579322414000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1953","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,11,7]]},"article-number":"R56"}}