Dyck Words, Lattice Paths, and Abelian Borders
Formal Languages and Automata Theory
2017-08-23 v1
Abstract
We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Mathematics, 2014). We also extend to any number of distinct abelian borders a result of Rampersad et al. (Developments in Language Theory, 2013) on the exact number of binary words of a given length with no abelian borders. Furthermore, we generalize these results to partial words.
Keywords
Cite
@article{arxiv.1708.06461,
title = {Dyck Words, Lattice Paths, and Abelian Borders},
author = {F. Blanchet-Sadri and Kun Chen and Kenneth Hawes},
journal= {arXiv preprint arXiv:1708.06461},
year = {2017}
}
Comments
In Proceedings AFL 2017, arXiv:1708.06226