Geodesic
Equivalence classes of mesh patterns with a dominating pattern
Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2.

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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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     author = {Tannock, Murray and Ulfarsson, Henning},
     title = {Equivalence classes of mesh patterns with a dominating pattern},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {2},
     year = {2017-2018},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-6/}
}
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Tannock, Murray; Ulfarsson, Henning. Equivalence classes of mesh patterns with a dominating pattern. Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2. doi : 10.23638/DMTCS-19-2-6. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-6/

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