Tree and Tripod Nim
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916092342960128 |
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| author | Hennessey, Aidan |
| author_facet | Hennessey, Aidan |
| contents | This paper introduces a variant of the impartial combinatorial game nim, called tree nim, as well as a particular case of tree nim called tripod nim. A certain existence-uniqueness result and a periodicity result are proven about the distribution of $\mathcal{P}$-positions and Grundy values in tree nim. Tripod nim is associated to a family of arrays similar to those which arise in the study of sequential compound games. Using these arrays, a partial analysis is given for tripod nim. Conjectures relating to the periods of the rows of these arrays are put forward. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07943 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tree and Tripod Nim Hennessey, Aidan Combinatorics This paper introduces a variant of the impartial combinatorial game nim, called tree nim, as well as a particular case of tree nim called tripod nim. A certain existence-uniqueness result and a periodicity result are proven about the distribution of $\mathcal{P}$-positions and Grundy values in tree nim. Tripod nim is associated to a family of arrays similar to those which arise in the study of sequential compound games. Using these arrays, a partial analysis is given for tripod nim. Conjectures relating to the periods of the rows of these arrays are put forward. |
| title | Tree and Tripod Nim |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.07943 |