On factor-free Dyck words with half-integer slope
Combinatorics
2018-06-26 v1
Abstract
We study a class of rational Dyck paths with slope (2m+1)/2 corresponding to factor-free Dyck words, as introduced by P. Duchon. We show that, for the slopes considered in this paper, the language of factor-free Dyck words is generated by an auxiliary language that we examine from the algebraic and combinatorial points of view. We provide a lattice path description of this language, and give an explicit enumeration formula in terms of partial Bell polynomials. As a corollary, we obtain new formulas for the number of associated factor-free generalized Dyck words.
Cite
@article{arxiv.1804.11244,
title = {On factor-free Dyck words with half-integer slope},
author = {Daniel Birmajer and Juan B. Gil and Michael D. Weiner},
journal= {arXiv preprint arXiv:1804.11244},
year = {2018}
}
Comments
13 pages. To appear in Advances in Applied Mathematics