Wilf classification of bi-vincular permutation patterns
classification
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patternsavoidingbi-vincularnumberpermutationsthreewilfaccording
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We classify all bi-vincular patterns of length two and three according to the number of permutations avoiding them. These patterns were recently defined by Bousquet-Melou et. al., and are natural generalizations of Babson and Steingrimsson's generalized patterns. The patterns are divided into seven and 24 Wilf classes, for lengths two and three, respectively. For most of the patterns an explicit form for the number of permutations avoiding the pattern is given.
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Equidistribution of mesh patterns of short length
Mesh patterns of length 2 fall into 105-108 equidistribution classes (conjectured 105), yielding a Wilf-class upper bound of 49 and resolving seven open counting problems.
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