Wilf-classification of mesh patterns of short length

2014/09/10 by Hilmarsson, Ísak, Jónsdóttir, Ingibjörg, Sigurðardóttir, Steinunn +2 · 2 citations
#05A05 #05A15 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.3165

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.

Cited by

• On fourteen equidistribution conjectures of Lv and Zhang and monotone mesh patterns with corner shadings
• Joint equidistributions of mesh patterns 123 and 132 with minus antipodal shadings

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