Successions in Words and Compositions

dc.contributor.author	Knopfmacher A.
dc.contributor.author	Munagi A.
dc.contributor.author	Wagner S.
dc.date.accessioned	2012-07-04T10:01:58Z
dc.date.available	2012-07-04T10:01:58Z
dc.date.issued	2012
dc.description.abstract	We consider words over the alphabet [k] = {1, 2, . . ., k}, k ≥ 2. For a fixed nonnegative integer p, a p-succession in a word w 1w 2 . . . w n consists of two consecutive letters of the form (w i, w i + p), i = 1, 2, . . ., n-1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the distribution of the number of p-successions in words of length n as n (and possibly k) tends to infinity; a simple instance of a phase transition (Gaussian-Poisson-degenerate) is encountered. Finally, we also investigate successions in compositions of integers. © 2012 Springer Basel AG.
dc.identifier.citation	Annals of Combinatorics
dc.identifier.citation	16
dc.identifier.citation	2
dc.identifier.citation	277
dc.identifier.citation	287
dc.identifier.issn	2180006
dc.identifier.other	doi:10.1007/s00026-012-0131-z
dc.identifier.uri	http://hdl.handle.net/10019.1/21539
dc.subject	compositions
dc.subject	limiting distributions
dc.subject	successions
dc.subject	words
dc.title	Successions in Words and Compositions
dc.type	Article