Avoiding patterns of length three in compositions and multiset permutations

Silvia Heubach; Toufik Mansour

doi:10.1016/j.aam.2005.06.005

Avoiding patterns of length three in compositions and multiset permutations

Silvia Heubach
, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We find generating functions for the number of compositions avoiding a single pattern or a pair of patterns of length three on the alphabet {1,2} and determine which of them are Wilf-equivalent on compositions. We also derive the number of permutations of a multiset which avoid these same patterns and determine the Wilf-equivalence of these patterns on permutations of multisets.

Original language	English
Pages (from-to)	156-174
Number of pages	19
Journal	Advances in Applied Mathematics
Volume	36
Issue number	2
DOIs	https://doi.org/10.1016/j.aam.2005.06.005
State	Published - Feb 2006

Bibliographical note

Funding Information:
We would like to thank H.S. Wilf for sending us a preprint of [6]. The second author also wants to express his gratitude to the Center for Computational Mathematics and Scientific Computation (CCMSC) for support of this research.

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aam.2005.06.005

Cite this

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abstract = "We find generating functions for the number of compositions avoiding a single pattern or a pair of patterns of length three on the alphabet \{1,2\} and determine which of them are Wilf-equivalent on compositions. We also derive the number of permutations of a multiset which avoid these same patterns and determine the Wilf-equivalence of these patterns on permutations of multisets.",

author = "Silvia Heubach and Toufik Mansour",

note = "Funding Information: We would like to thank H.S. Wilf for sending us a preprint of [6]. The second author also wants to express his gratitude to the Center for Computational Mathematics and Scientific Computation (CCMSC) for support of this research.",

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PY - 2006/2

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N2 - We find generating functions for the number of compositions avoiding a single pattern or a pair of patterns of length three on the alphabet {1,2} and determine which of them are Wilf-equivalent on compositions. We also derive the number of permutations of a multiset which avoid these same patterns and determine the Wilf-equivalence of these patterns on permutations of multisets.

AB - We find generating functions for the number of compositions avoiding a single pattern or a pair of patterns of length three on the alphabet {1,2} and determine which of them are Wilf-equivalent on compositions. We also derive the number of permutations of a multiset which avoid these same patterns and determine the Wilf-equivalence of these patterns on permutations of multisets.

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U2 - 10.1016/j.aam.2005.06.005

DO - 10.1016/j.aam.2005.06.005

M3 - Article

AN - SCOPUS:31544436897

SN - 0196-8858

VL - 36

SP - 156

EP - 174

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

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ER -

Avoiding patterns of length three in compositions and multiset permutations

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

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