New equivalences for pattern avoiding involutions

W. M.B. Dukes; Vít Jelínek; Toufik Mansour; Astrid Reifegerste

doi:10.1090/S0002-9939-08-09492-6

New equivalences for pattern avoiding involutions

W. M.B. Dukes, Vít Jelínek, Toufik Mansour, Astrid Reifegerste

Department of Mathematics

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

Abstract

We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S₅, S₆, and S₇ for involutions.

Original language	English
Pages (from-to)	457-465
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-08-09492-6
State	Published - Feb 2009

Keywords

Forbidden subsequences
Pattern avoiding involutions
Pattern avoiding permutations
Signed permutations
Wilf equivalence

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-08-09492-6

Cite this

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abstract = "We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for involutions.",

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AU - Mansour, Toufik

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N2 - We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for involutions.

AB - We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for involutions.

KW - Forbidden subsequences

KW - Pattern avoiding involutions

KW - Pattern avoiding permutations

KW - Signed permutations

KW - Wilf equivalence

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New equivalences for pattern avoiding involutions

Abstract

Keywords

ASJC Scopus subject areas

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