Discrete Mathematics & Theoretical Computer Science, Vol 11, No 1 (2009)

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The distribution of ascents of size d or more in compositions

Charlotte Alix Brennan, Arnold Knopfmacher


A composition of a positive integer n is a finite sequence of positive integers a1, a2, …, ak such that a1+a2+⋯+ak=n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more if ai+1 ≥ai+d. We determine the mean, variance and limiting distribution of the number of ascents of size d or more in the set of compositions of n. We also study the average size of the greatest ascent over all compositions of n.

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