### The distribution of ascents of size d or more in compositions

*Charlotte Alix Brennan, Arnold Knopfmacher*

#### 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.Full Text: PDF PostScript