New equivalences for pattern avoiding involutions

2007/08/10 by Dukes, Mark, Jelínek, Vit, Mansour, Toufik +1
#05A05 #05A15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0708.1357

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.

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