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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New equivalences for pattern avoiding involutions
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by W. M. B. Dukes, Vít Jelinek, Toufik Mansour and Astrid Reifegerste PDF
Proc. Amer. Math. Soc. 137 (2009), 457-465 Request permission

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
  • Email: dukes@raunvis.hi.is
  • Vít Jelinek
  • Affiliation: Department of Applied Mathematics, Charles University, Prague, Czech Republic
  • Email: jelinek@kam.mff.cuni.cz
  • Toufik Mansour
  • Affiliation: Department of Mathematics, University of Haifa, 31905 Haifa, Israel
  • Email: toufik@math.haifa.ac.il
  • Astrid Reifegerste
  • Affiliation: Faculty of Mathematics, University of Magdeburg, Magdeburg, Germany
  • Email: astrid.reifegerste@ovgu.de
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 457-465
  • MSC (2000): Primary 05A15; Secondary 05A05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09492-6
  • MathSciNet review: 2448564