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.

Source : oai:HAL:hal-00988184v1

Volume: Vol. 11 no. 1

Section: Combinatorics

Published on: January 1, 2009

Submitted on: March 26, 2015

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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