The goal of this paper is to Wilf-classify mesh patterns of length 2. To this end we prove The Shading Lemma, which gives sufficient conditions for two mesh patterns to be coincident (i.e., avoided by the same permutations) and therefore Wilf-equivalent. The lemma, along with other rules which implie Wilf-coincidence we show that there are at most 56 Wilf-classes of mesh patterns of length 2. We conjecture that the exact number is 46 and hope to revisit this area and prove this conjecture.

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• Electronic Journal of Combinatorics, Volume 22 (2015)
  
• arXiv (Note: Same as journal version except for a minor modification in the paragraph under Table 1, p. 11)
  

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