Wilf classification of bi-vincular permutation patterns

2009/10/27 by Parviainen, Robert
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.5103

Abstract

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.

Related

• Some Wilf-equivalences for vincular patterns
• A New Class of Wilf-Equivalent Permutations
• Enumeration schemes for vincular patterns
• A Wilf equivalence related to two stack sortable permutations
• Enumerating permutations avoiding more than three Babson - Steingr'ımsson patterns