{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:12:40Z","timestamp":1772514760181,"version":"3.50.1"},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5855,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1992,9]]},"abstract":"<jats:p>Let \u03c3, \u03c0 be two permutations selected at random from the uniform distribution on the symmetric group <jats:italic>S<jats:sub>n<\/jats:sub><\/jats:italic>. By a result of Dixon [5], the subgroup <jats:italic>G<\/jats:italic> generated by \u03c3, \u03c0 is almost always (i.e. with probability approaching 1 as <jats:italic>n<\/jats:italic> \u2192 \u221e) either <jats:italic>S<jats:sub>n<\/jats:sub><\/jats:italic> or the alternating group <jats:italic>A<jats:sub>n<\/jats:sub><\/jats:italic>. We prove that the diameter of the Cayley graph of <jats:italic>G<\/jats:italic> defined by {\u03c3, \u03c0} is almost always not greater than exp ((\u00bd + <jats:italic>o<\/jats:italic>(l)). (In <jats:italic>n<\/jats:italic>)<jats:sup>2<\/jats:sup>).<\/jats:p>","DOI":"10.1017\/s0963548300000237","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T07:19:03Z","timestamp":1221203943000},"page":"201-208","source":"Crossref","is-referenced-by-count":6,"title":["On the Diameter of Random Cayley Graphs of the Symmetric Group"],"prefix":"10.1017","volume":"1","author":[{"given":"L.","family":"Babai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. L.","family":"Hetyei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300000237_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90068-X"},{"key":"S0963548300000237_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(88)90033-7"},{"key":"S0963548300000237_ref003","first-page":"857","volume-title":"Proc. 31st IEEE Symp. on Foundations of Computer Science","author":"Babai","year":"1990"},{"key":"S0963548300000237_ref004","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/12.1.47"},{"key":"S0963548300000237_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF00536750"},{"key":"S0963548300000237_ref008","first-page":"3","article-title":"On the Field of Combinatory Analysis","volume":"8","author":"Goncharov","year":"1944","journal-title":"Isvestija Akad. Nauk. SSSR"},{"key":"S0963548300000237_ref009","volume-title":"An Introduction to the Theory of Numbers","author":"Hardy","year":"1960"},{"key":"S0963548300000237_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02020968"},{"key":"S0963548300000237_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01110210"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300000237","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T16:51:38Z","timestamp":1558025498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300000237\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,9]]}},"alternative-id":["S0963548300000237"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300000237","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,9]]}}}