Enumerating runs, valleys, and peaks in Catalan words
Combinatorics
2024-04-09 v1
Abstract
We provide generating functions, formulas, and asymptotic expressions for the number of Catalan words based on the number of runs of ascents (descents), runs of weak ascents (descents), -valleys, valleys, symmetric valleys, -peaks, peaks, and symmetric peaks. We also establish some bijections with restricted Dyck paths and ordered trees that transports some statistics.
Cite
@article{arxiv.2404.05672,
title = {Enumerating runs, valleys, and peaks in Catalan words},
author = {Jean-Luc Baril and Pamela E. Harris and Kimberly J. Harry and Matt McClinton and José L. Ramírez},
journal= {arXiv preprint arXiv:2404.05672},
year = {2024}
}