Equivalence Classes Induced by Binary Tree Isomorphism -- Generating Functions
Abstract
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree \cite{abboud2018subtree}. Binary tree isomorphism is an important problem in computer science. The enumeration of the number of non-isomorphic rooted binary trees is therefore well known. The paper reiterates the known results for ordered binary trees and presents previous results for the enumeration of non-isomorphic rooted binary trees. Then, new enumeration results are put forward for two-colour binary tree isomorphism parametrized by the number of nodes, the number of specific colours and the number of non-isomorphic sibling subtrees. Multi-variate generating function equations are presented that enumerate these tree structures. The generating functions with these parametrizations separate multiplicatively into simplified generating function equations.
Keywords
Cite
@article{arxiv.2503.02663,
title = {Equivalence Classes Induced by Binary Tree Isomorphism -- Generating Functions},
author = {David Serena and William J Buchanan},
journal= {arXiv preprint arXiv:2503.02663},
year = {2025}
}