Equivalence classes of mesh patterns with a dominating pattern
Discrete Mathematics & Theoretical Computer Science, February 9, 2018, Vol. 19 no. 2, Permutation Patterns 2016
Two mesh patterns are coincident if they are avoided by the same set of
permutations, and are Wilf-equivalent if they have the same number of avoiders
of each length. We provide sufficient conditions for coincidence of mesh
patterns, when only permutations also avoiding a longer classical pattern are
considered. Using these conditions we completely classify coincidences between
families containing a mesh pattern of length 2 and a classical pattern of
length 3. Furthermore, we completely Wilf-classify mesh patterns of length 2
inside the class of 231-avoiding permutations.
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- Discrete Mathematics & Theoretical Computer Science, February 9, 2018, Vol. 19 no. 2, Permutation Patterns 2016
- arXiv