{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:46:42Z","timestamp":1758476802824},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T00:00:00Z","timestamp":1523491200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:p>We study the number of random permutations needed to invariably generate the symmetric group <jats:italic>S<jats:sub>n<\/jats:sub><\/jats:italic> when the distribution of cycle counts has the strong \u03b1-logarithmic property. The canonical example is the Ewens sampling formula, for which the special case \u03b1 = 1 corresponds to uniformly random permutations.<\/jats:p><jats:p>For strong \u03b1-logarithmic measures and almost every \u03b1, we show that precisely \u2308(1\u2212\u03b1log2)<jats:sup>\u22121<\/jats:sup>\u2309 permutations are needed to invariably generate <jats:italic>S<jats:sub>n<\/jats:sub><\/jats:italic> with asymptotically positive probability. A corollary is that for many other probability measures on <jats:italic>S<jats:sub>n<\/jats:sub><\/jats:italic> no fixed number of permutations will invariably generate <jats:italic>S<jats:sub>n<\/jats:sub><\/jats:italic> with positive probability. Along the way we generalize classic theorems of Erd\u0151s, Tehran, Pyber, \u0141uczak and Bovey to permutations obtained from the Ewens sampling formula.<\/jats:p>","DOI":"10.1017\/s096354831800007x","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T09:52:23Z","timestamp":1523526743000},"page":"853-891","source":"Crossref","is-referenced-by-count":0,"title":["Ewens Sampling and Invariable Generation"],"prefix":"10.1017","volume":"27","author":[{"given":"GERANDY","family":"BRITO","sequence":"first","affiliation":[]},{"given":"CHRISTOPHER","family":"FOWLER","sequence":"additional","affiliation":[]},{"given":"MATTHEW","family":"JUNGE","sequence":"additional","affiliation":[]},{"given":"AVI","family":"LEVY","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,4,12]]},"reference":[{"key":"S096354831800007X_ref30","doi-asserted-by":"publisher","DOI":"10.1145\/322063.322071"},{"key":"S096354831800007X_ref18","first-page":"160","article-title":"Observationes circa series infinitas.","volume":"9","author":"Euler","year":"1737","journal-title":"Commentarii Academiae Scientarum Petropolitanae"},{"key":"S096354831800007X_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/15-STS529"},{"key":"S096354831800007X_ref25","unstructured":"Kenyon R. , Kral D. , Radin C. and Winkler P. 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