On the enumeration of records of rooted trees and rooted forests
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866914092086722560 |
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| author | Lillo, Adrián Rosas, Mercedes Trandafir, Stefan |
| author_facet | Lillo, Adrián Rosas, Mercedes Trandafir, Stefan |
| contents | A record of a rooted Cayley tree is a node whose label is the largest along the unique path to the root. In this work, we find elegant functional equations relating the generating functions for records of rooted Cayley trees and for records of forests of rooted trees with the Cayley tree function, and explore the consequences of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the enumeration of records of rooted trees and rooted forests Lillo, Adrián Rosas, Mercedes Trandafir, Stefan Combinatorics 05A15 (Primary) 05A19 (Secondary) A record of a rooted Cayley tree is a node whose label is the largest along the unique path to the root. In this work, we find elegant functional equations relating the generating functions for records of rooted Cayley trees and for records of forests of rooted trees with the Cayley tree function, and explore the consequences of our results. |
| title | On the enumeration of records of rooted trees and rooted forests |
| topic | Combinatorics 05A15 (Primary) 05A19 (Secondary) |
| url | https://arxiv.org/abs/2510.12536 |