Wilf-Classification of Mesh Patterns of Short Length

Ísak Hilmarsson, Ingibjörg Jónsdóttir, Steinunn Sigurðardóttir, Lína Viðarsdóttir, Henning Ulfarsson

Abstract


This paper starts the Wilf-classification of mesh patterns of length 2. Although there are initially 1024 patterns to consider we introduce automatic methods to reduce the number of potentially different Wilf-classes to at most 65. By enumerating some of the remaining classes we bring that upper-bound further down to 56. Finally, we conjecture that the actual number of Wilf-classes of mesh patterns of length 2 is 46.


Keywords


Permutations; Pattern avoidance; Generating functions

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