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.
https://hal.inria.fr/hal-00988184
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s
<>
Soumis le : mercredi 7 mai 2014 - 16:13:13
Dernière modification le : mardi 17 octobre 2017 - 01:03:22
Document(s) archivé(s) le : jeudi 7 août 2014 - 11:35:12
Charlotte Brennan, Arnold Knopfmacher. The distribution of ascents of size d or more in compositions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 11 (1), pp.1--10. 〈hal-00988184〉
