The 26 Wilf-equivalence classes of length five quasi-consecutive patterns

Abstract

We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$. We then prove additional equivalences to explicitly classify all quasi-consecutive patterns of length $5$ into 26 Wilf-equivalence classes.

Keywords

• mathematics - combinatorics
• 05a05, 05a19
• g.2.1