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

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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",

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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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Avoiding patterns of length three in compositions and multiset permutations

Abstract

Bibliographical note

ASJC Scopus subject areas

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