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 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.
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