## Charlotte Brennan ; Arnold Knopfmacher - The distribution of ascents of size d or more in compositions

dmtcs:462 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, Vol. 11 no. 1 - https://doi.org/10.46298/dmtcs.462
The distribution of ascents of size d or more in compositionsArticle

Authors: Charlotte Brennan 1; Arnold Knopfmacher 2

• 1 School of Mathematics [Johannesburg]
• 2 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]

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.

Volume: Vol. 11 no. 1
Section: Combinatorics
Published on: January 1, 2009
Imported on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]