Wilf-classification of mesh patterns of short length
  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. 
\'Isak Hilmarsson, Ingibj\"org J\'onsd\'ottir, Steinunn   Sigur{\dh}ard\'ottir, L\'ina Vi{\dh}arsd\'ottir and Henning Ulfarsson
math.CO cs.DM