Chip-Firing on Infinite $k$-ary Trees
Fuente:
arXiv
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| Autori principali: | , , , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866910780925935616 |
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| author | Agrawal, Dillan Ge, Selena Greene, Jate Khovanova, Tanya Kim, Dohun Mandal, Rajarshi Parida, Tanish Pulugurtha, Anirudh Redwine, Gordon Samanta, Soham Xu, Albert |
| author_facet | Agrawal, Dillan Ge, Selena Greene, Jate Khovanova, Tanya Kim, Dohun Mandal, Rajarshi Parida, Tanish Pulugurtha, Anirudh Redwine, Gordon Samanta, Soham Xu, Albert |
| contents | We use an infinite $k$-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with $N$ chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given $k$ as a function of $N$ and study its properties. We do the same for the total number of fires. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chip-Firing on Infinite $k$-ary Trees Agrawal, Dillan Ge, Selena Greene, Jate Khovanova, Tanya Kim, Dohun Mandal, Rajarshi Parida, Tanish Pulugurtha, Anirudh Redwine, Gordon Samanta, Soham Xu, Albert Combinatorics 05C57, 05C63 We use an infinite $k$-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with $N$ chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given $k$ as a function of $N$ and study its properties. We do the same for the total number of fires. |
| title | Chip-Firing on Infinite $k$-ary Trees |
| topic | Combinatorics 05C57, 05C63 |
| url | https://arxiv.org/abs/2501.06675 |