Binary words avoiding xx^Rx and strongly unimodal sequences

James D. Currie; Narad Rampersad

Binary words avoiding xx^Rx and strongly unimodal sequences

Combinatorics 2015-08-13 v1 Formal Languages and Automata Theory

Authors: James D. Currie , Narad Rampersad

Abstract

In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxx^R was intermediate between polynomial and exponential. We now show that the same holds for the growth of the number of binary words avoiding the pattern xx^Rx. Curiously, the analysis for xx^Rx is much simpler than that for xxx^R. We derive our results by giving a bijection between the set of binary words avoiding xx^Rx and a class of sequences closely related to the class of "strongly unimodal sequences."

Keywords

sturmian words and combinatorics on words pattern avoidance in permutations

Cite

@article{arxiv.1508.02964,
  title  = {Binary words avoiding xx^Rx and strongly unimodal sequences},
  author = {James D. Currie and Narad Rampersad},
  journal= {arXiv preprint arXiv:1508.02964},
  year   = {2015}
}