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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.02663 |
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| _version_ | 1866929740699402240 |
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| author | Serena, David Buchanan, William J |
| author_facet | Serena, David Buchanan, William J |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence Classes Induced by Binary Tree Isomorphism -- Generating Functions Serena, David Buchanan, William J Combinatorics Numerical Analysis 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. |
| title | Equivalence Classes Induced by Binary Tree Isomorphism -- Generating Functions |
| topic | Combinatorics Numerical Analysis |
| url | https://arxiv.org/abs/2503.02663 |