Enumeration of 3-letter patterns in compositions
Combinatorics
2007-05-23 v1
Abstract
Let A be any set of positive integers and n a positive integer. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with m parts in A that have r occurrences of 3-letter patterns formed by two (adjacent) instances of levels, rises and drops. We also derive asymptotics for the number of compositions of n that avoid a given pattern. Finally, we obtain the generating function for the number of k-ary words of length m which contain a prescribed number of occurrences of a given pattern as a special case of our results.
Keywords
Cite
@article{arxiv.math/0603285,
title = {Enumeration of 3-letter patterns in compositions},
author = {S. Heubach and T. Mansour},
journal= {arXiv preprint arXiv:math/0603285},
year = {2007}
}
Comments
20 pages, 1 figure; accepted for the Proceedings of the 2005 Integer Conference