Two Enumerative Results on Cycles of Permutations

dc.creatorStanley, Richard P.
dc.date2009-01-14
dc.date.accessioned2026-07-07T12:29:31Z
dc.date.available2026-07-07T12:29:31Z
dc.descriptionAnswering a question of Bona, it is shown that for n>1 the probability that 1 and 2 are in the same cycle of a product of two n-cycles on the set {1,2,...,n} is 1/2 if n is odd and 1/2 - 2/(n-1){n+2) if n is even. Another result concerns the generating function P_h(q) for the number of cycles of the product (1,2,...,n)w, where w ranges over all permutations of 1,2,...,n of cycle type h. A formula is obtained for P_h(q) from which it is proved that the zeros of P_h(q) have real part 0.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0901.2008
dc.identifierhttp://arxiv.org/abs/0901.2008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215904
dc.subjectCombinatorics
dc.subject05A15; 05E05
dc.titleTwo Enumerative Results on Cycles of Permutations
dc.typetext

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