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  1. Home > Articles & Issues >
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Conference paper

Equivalences for pattern avoiding involutions and classification

Mark Dukes ORCID (1) (2), Vít Jelínek ORCID (3), Toufik Mansour ORCID (4), Astrid Reifegerste (5)
(1) Science Institute, University of Iceland
(2) University of Iceland [Reykjavik]
(3) Department of Applied Mathematics (KAM)
(4) Department of Mathematics [Haïfa]
(5) Faculty of Mathematics
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Proceedings
DOI
10.46298/dmtcs.3637
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Equivalences for pattern avoiding involutions and classification

Mark Dukes ORCID (1) (2), Vít Jelínek ORCID (3), Toufik Mansour ORCID (4), Astrid Reifegerste (5)
(1) Science Institute, University of Iceland
(2) University of Iceland [Reykjavik]
(3) Department of Applied Mathematics (KAM)
(4) Department of Mathematics [Haïfa]
(5) Faculty of Mathematics
Abstract
English
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 $S_5$, $S_6$, and $S_7$ for both permutations and involutions.
French
Nous complétons la classification de Wilf des motifs signés de longueur 5 à la fois pour les permutations signées et les involutions signées. Nous donnons de nouvelles équivalences générales de motifs qui prouvent les conjectures de Jaggard concernant les involutions dans le groupe symétrique évitant certains motifs de longueur 5 et 6. De cette manière nous complétons également la classification de Wilf de $S_5$, $S_6$ et $S_7$ à la fois pour les permutations et les involutions.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • forbidden subsequences
  • pattern avoiding permutations
  • pattern avoiding involutions
  • signed permutations
  • Wilf equivalence
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