Journal of Combinatorics
Volume 6 (2015)
Some Wilf-equivalences for vincular patterns
Pages: 19 – 45
We prove several Wilf-equivalences for vincular patterns of length $4$, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating functions for the number of permutations of length $n$ avoiding a single pattern for the patterns 124-3, 134-2, 231-4, 241-3, 132-4, and 142-3. This nearly completes the Wilf-classification of vincular patterns of length 4. As a corollary, these results imply Wilf-equivalences for certain barred patterns of length 5 with a single bar.
permutations, pattern avoidance, vincular pattern, Wilf-equivalence