Logo image
Back
Enumeration and asymptotics of restricted compositions having the same number of parts
Journal article   Open access   Peer reviewed

Enumeration and asymptotics of restricted compositions having the same number of parts

Cyril Banderier and Paweł Hitczenko
Discrete Applied Mathematics, v 160(18), pp 2542-2554
Dec 2012
DOI: https://doi.org/10.1016/j.dam.2011.12.011
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
https://doi.org/10.1016/j.dam.2011.12.011View
Published, Version of Record (VoR) Open

Abstract

Asymptotics of [formula omitted]-finite sequences Diagonal of algebraic generating function Pairs of combinatorial structures Local limit theorem Integer composition
We study pairs and m-tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of parts. Under the uniform probability model, we obtain the asymptotics for the probability that two or, more generally, m randomly and independently chosen compositions of n have the same number of parts. For a large class of compositions, we show how a nice interplay between complex analysis and probability theory allows to get full asymptotics for this probability. Our results extend an earlier work of Bóna and Knopfmacher. While we restrict our attention to compositions, our approach is also of interest for tuples of other combinatorial structures having the same number of parts.

Metrics

7 Record Views
15 citations in Web of Science
13 citations in Scopus

Details

UN Sustainable Development Goals (SDGs)

This publication has contributed to the advancement of the following goals:

#4 Quality Education

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Mathematics, Applied
Logo image