Growth and density in free groupoids
Combinatorics
2024-07-24 v2
Abstract
The density of a subgroupoid with respect to a free groupoid is defined as the asymptotic ratio of their growths. This notion can be interpreted as a generalisation of the index's inverse for groups or as the probability of an element belonging to a subgroupoid. This more combinatorial strategy shows a richer picture of free groupoids than the bare algebraic perspective. We study the growth and density of several subgroupoids of a free groupoid. In addition, some aspects of enumeration related to the Motzkin paths are shown.
Cite
@article{arxiv.2401.07827,
title = {Growth and density in free groupoids},
author = {Carles Cardó},
journal= {arXiv preprint arXiv:2401.07827},
year = {2024}
}
Comments
17 pages, 4 figures, Under review at European Journal of combinatorics