Enumeration of 3-letter patterns in compositions

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint 23 Mar 2012Embargo end date: 01 Mar 2006Publisher:DE GRUYTER

Authors: Heubach, S.; Mansour, T.;

doi: 10.1515/9783110925098.243 , 10.5281/zenodo.8346964 , 10.48550/arxiv.math/0603285 , 10.5281/zenodo.8346963

arXiv: math/0603285

Enumeration of 3-letter patterns in compositions

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Abstract

Let A be any set of positive integers and n ∈ N. 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.

Related Organizations

California State University Los Angeles
United States
University of Haifa
Israel

Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A05 (primary), 05A15, 05A16 (secondary)

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