The Sandpile Group of a Cone Over a Bi-Coconut Tree
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908846124957696 |
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| author | Smith, Dorian |
| author_facet | Smith, Dorian |
| contents | The sandpile group of a connected graph is a finite abelian group whose cardinality is the number of spanning trees in the graph. We compute the spanning tree number and sandpile group structure for the cone over a bi-coconut tree, generalizing work of Reiner and Smith on the cone over a coconut tree. We also answer one of their questions, by exhibiting a family of trees whose sandpile groups are all cyclic but their number of leaves grows without bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Sandpile Group of a Cone Over a Bi-Coconut Tree Smith, Dorian Combinatorics 05C50, 05C25 The sandpile group of a connected graph is a finite abelian group whose cardinality is the number of spanning trees in the graph. We compute the spanning tree number and sandpile group structure for the cone over a bi-coconut tree, generalizing work of Reiner and Smith on the cone over a coconut tree. We also answer one of their questions, by exhibiting a family of trees whose sandpile groups are all cyclic but their number of leaves grows without bound. |
| title | The Sandpile Group of a Cone Over a Bi-Coconut Tree |
| topic | Combinatorics 05C50, 05C25 |
| url | https://arxiv.org/abs/2602.18621 |