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Equivalences for pattern avoiding involutions and classification

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 both permutations and involutions.
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Mark Dukes, Vít Jelínek, Toufik Mansour, Astrid Reifegerste. Equivalences for pattern avoiding involutions and classification. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Vi–a del Mar, Chile. pp.181-188. ⟨hal-01185172⟩

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