A note on Puder's generalised co-growth formula for trees
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917917510074368 |
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| author | Li, Wenbo Thomas, Joe |
| author_facet | Li, Wenbo Thomas, Joe |
| contents | In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an operator version of the co-growth formula. We also provide a simpler proof of Puder's generalised co-growth formula for the regular tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Puder's generalised co-growth formula for trees Li, Wenbo Thomas, Joe Combinatorics 05C05 In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an operator version of the co-growth formula. We also provide a simpler proof of Puder's generalised co-growth formula for the regular tree. |
| title | A note on Puder's generalised co-growth formula for trees |
| topic | Combinatorics 05C05 |
| url | https://arxiv.org/abs/2502.06372 |