Wilf-Classification of Mesh Patterns of Short Length

  • Ísak Hilmarsson
  • Ingibjörg Jónsdóttir
  • Steinunn Sigurðardóttir
  • Lína Viðarsdóttir
  • Henning Ulfarsson
Keywords: Permutations, Pattern avoidance, Generating functions


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.

Author Biographies

Steinunn Sigurðardóttir
Reykjavik University
Lína Viðarsdóttir
Reykjavik University
Article Number