The most and the least avoided consecutive patterns
Combinatorics
2014-02-26 v1
Abstract
We prove that the number of permutations avoiding an arbitrary consecutive pattern of length m is asymptotically largest when the avoided pattern is 12...m, and smallest when the avoided pattern is 12...(m-2)m(m-1). This settles a conjecture of the author and Noy from 2001, as well as another recent conjecture of Nakamura. We also show that among non-overlapping patterns of length m, the pattern 134...m2 is the one for which the number of permutations avoiding it is asymptotically largest.
Cite
@article{arxiv.1203.1636,
title = {The most and the least avoided consecutive patterns},
author = {Sergi Elizalde},
journal= {arXiv preprint arXiv:1203.1636},
year = {2014}
}