Enumeration of multi-rooted plane trees
Combinatorics
2024-02-06 v3
Abstract
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We also propose recursion relations for numbers of such trees as well as for the corresponding generating functions. Explicit expressions for the generating functions corresponding to plane trees having two and three roots are derived. As a by-product, we obtain a new binomial identity and a conjecture relating hypergeometric functions.
Keywords
Cite
@article{arxiv.2301.09765,
title = {Enumeration of multi-rooted plane trees},
author = {Anwar Al Ghabra and K. Gopala Krishna and Patrick Labelle and Vasilisa Shramchenko},
journal= {arXiv preprint arXiv:2301.09765},
year = {2024}
}
Comments
28 pages, 3 figures