Pattern-avoiding alternating words
Combinatorics
2015-05-18 v1
Abstract
A word is alternating if either (when the word is up-down) or (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset. Further, we show that the number of 123-avoiding up-down words of even length is given by the Narayana numbers, which is also the case, shown by us bijectively, with 132-avoiding up-down words of even length. We also give formulas for enumerating all other cases of avoidance of a permutation pattern of length 3 on alternating words.
Cite
@article{arxiv.1505.04078,
title = {Pattern-avoiding alternating words},
author = {Emma L. L. Gao and Sergey Kitaev and Philip B. Zhang},
journal= {arXiv preprint arXiv:1505.04078},
year = {2015}
}