Factorization of Dyck words and the distribution of the divisors of an integer
José Manuel Rodríguez Caballero · arXiv (Cornell University) · 2017
In [CaballeroHooleyDelta], we associated a Dyck word $\langle\! \langle n \rangle\! \rangle_λ$ to any pair $(n, λ)$ consisting of an integer $n \geq 1$ and a real number $λ> 1$. The goal of the present paper is to show a relationship between the factorization of $\langle\! \langle n \rangle\! \rangle_λ$ as the concatenation of irreducible Dyck words and the distribution of the divisors of $n$. In particular, we will provide a characterization of $λ$-densely divisible numbers (these numbers were introduced in [castryck2014new]).