Successions in Words and Compositions |
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Authors: | Arnold Knopfmacher Augustine Munagi Stephan Wagner |
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Affiliation: | 1. The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, South Africa 2. Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, 7602, Stellenbosch, South Africa
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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 1 w 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. |
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