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New equivalences for pattern avoiding involutions

Authors: W. M. B. Dukes, V\’ it Jel\’ inek, Toufik Mansour and Astrid Reifegerste
Journal: Proc. Amer. Math. Soc. 137 (2009), 457-465
MSC (2000): Primary 05A15; Secondary 05A05
Published electronically: July 9, 2008
MathSciNet review: 2448564
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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 $ S_5$, $ S_6$, and $ S_7$ for involutions.

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Additional Information

W. M. B. Dukes
Affiliation: Science Institute, University of Iceland, Reykjavík, Iceland

V\’ it Jel\’ inek
Affiliation: Department of Applied Mathematics, Charles University, Prague, Czech Republic

Toufik Mansour
Affiliation: Department of Mathematics, University of Haifa, 31905 Haifa, Israel

Astrid Reifegerste
Affiliation: Faculty of Mathematics, University of Magdeburg, Magdeburg, Germany

Keywords: Forbidden subsequences, pattern avoiding permutations, pattern avoiding involutions, signed permutations, Wilf equivalence
Received by editor(s): November 21, 2007
Received by editor(s) in revised form: January 22, 2008
Published electronically: July 9, 2008
Additional Notes: The second author was supported by project 201/05/H014 of the Czech Science Foundation and project MSM0021620838 of the Czech Ministry of Education.
Communicated by: Jim Haglund
Article copyright: © Copyright 2008 American Mathematical Society

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