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The distribution of ascents of size d or more in compositions

Abstract : A composition of a positive integer n is a finite sequence of positive integers a(1), a(2), ..., a(k) such that a(1) + a(2) + ... + a(k) = n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more if a(i+1) >= a(i) + 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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Charlotte Brennan, Arnold Knopfmacher. The distribution of ascents of size d or more in compositions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, Vol. 11 no. 1 (1), pp.1--10. ⟨10.46298/dmtcs.462⟩. ⟨hal-00988184⟩

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