Wilf classification of bi-vincular permutation patterns

Details Wilf classification of bi-vincular permutation patterns Wilf classification of bi-vincular permutation patterns

2009-10-27

arxiv.org/abs/0910.5103v2

Mathematics

Combinatorics

Changed name of patterns to bi-vincular to confirm with new standard. Answered Question 2 and solved Conjecture 18. 16 pages,

Scientific paper

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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