Some Wilf-equivalences for vincular patterns
Combinatorics
2014-08-26 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1309.7111,
title = {Some Wilf-equivalences for vincular patterns},
author = {Andrew M. Baxter and Mark Shattuck},
journal= {arXiv preprint arXiv:1309.7111},
year = {2014}
}
Comments
20 pages. To appear in the Journal of Combinatorics, Special Issue for the Proceedings of Permutation Patterns 2013