Bivariate generating functions for involutions restricted by 3412

Eric S. Egge; Toufik Mansour

doi:10.1016/j.aam.2005.01.005

Bivariate generating functions for involutions restricted by 3412

Eric S. Egge, Toufik Mansour

Department of Mathematics

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

Abstract

We study bivariate generating functions for the number of involutions in Sn subject to two restrictions. One restriction is that the involution avoid 3412 or contain 3412 exactly once. The other restriction is that the involution avoid another pattern π or contain π exactly once. In many cases we express these generating functions in terms of Chebyshev polynomials of the second kind.

Original language	English
Pages (from-to)	118-137
Number of pages	20
Journal	Advances in Applied Mathematics
Volume	36
Issue number	2
DOIs	https://doi.org/10.1016/j.aam.2005.01.005
State	Published - Feb 2006

Keywords

Chebyshev polynomial
Forbidden subsequence
Pattern-avoiding permutation
Restricted involution
Restricted permutation

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2005.01.005

Cite this

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abstract = "We study bivariate generating functions for the number of involutions in Sn subject to two restrictions. One restriction is that the involution avoid 3412 or contain 3412 exactly once. The other restriction is that the involution avoid another pattern π or contain π exactly once. In many cases we express these generating functions in terms of Chebyshev polynomials of the second kind.",

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AB - We study bivariate generating functions for the number of involutions in Sn subject to two restrictions. One restriction is that the involution avoid 3412 or contain 3412 exactly once. The other restriction is that the involution avoid another pattern π or contain π exactly once. In many cases we express these generating functions in terms of Chebyshev polynomials of the second kind.

KW - Chebyshev polynomial

KW - Forbidden subsequence

KW - Pattern-avoiding permutation

KW - Restricted involution

KW - Restricted permutation

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JO - Advances in Applied Mathematics

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ER -

Bivariate generating functions for involutions restricted by 3412

Abstract

Keywords

ASJC Scopus subject areas

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