Self-Reachable Chip Configurations on Trees
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912010676994048 |
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| author | Lyons, Benjamin Olsen, McCabe |
| author_facet | Lyons, Benjamin Olsen, McCabe |
| contents | In this paper, we explore the notion of a \emph{self-reachable} chip configuration on a simple graph, that is a chip configuration which can be re-obtained from itself after a (nonempty) sequence of vertex firings. In particular, we focus on the case of trees and provide a characterization for such configurations, as well as show that all self-reachable configurations with the same number of chips on a tree are reachable from one another. We conclude with a recursive enumeration formula for the number of self-reachable configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-Reachable Chip Configurations on Trees Lyons, Benjamin Olsen, McCabe Combinatorics 05C57, 05C05 In this paper, we explore the notion of a \emph{self-reachable} chip configuration on a simple graph, that is a chip configuration which can be re-obtained from itself after a (nonempty) sequence of vertex firings. In particular, we focus on the case of trees and provide a characterization for such configurations, as well as show that all self-reachable configurations with the same number of chips on a tree are reachable from one another. We conclude with a recursive enumeration formula for the number of self-reachable configurations. |
| title | Self-Reachable Chip Configurations on Trees |
| topic | Combinatorics 05C57, 05C05 |
| url | https://arxiv.org/abs/2409.00763 |