Equivalences for pattern avoiding involutions and classification

Dukes, Mark and Jelinek, Vıt and Mansour, Toufik and Reifegerste, Astrid (2008) Equivalences for pattern avoiding involutions and classification. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 181-188.

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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 both permutations and involutions.