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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2509.21744 |
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| _version_ | 1866915695885811712 |
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| author | Kusakari, Keiichirou Abuku, Tomoaki |
| author_facet | Kusakari, Keiichirou Abuku, Tomoaki |
| contents | We investigate conditions under which positions in combinatorial games admit simple values. We introduce a unified diamond framework, the $\Diamond_A$-property ($A\in\{\mathbb{Z},\mathbb{D}$), for sets of positions closed under options. Under certain conditions, this framework guarantees that all values are integers, dyadic rationals, or pairs $\{m|n\}$ (on $\mathbb{Z}$ or $\mathbb{D}$). As an application, we establish that every position in \textsc{Yashima} game on bipartite graphs has an integer pair value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Various Diamond Properties in Combinatorial Game Theory Kusakari, Keiichirou Abuku, Tomoaki Combinatorics We investigate conditions under which positions in combinatorial games admit simple values. We introduce a unified diamond framework, the $\Diamond_A$-property ($A\in\{\mathbb{Z},\mathbb{D}$), for sets of positions closed under options. Under certain conditions, this framework guarantees that all values are integers, dyadic rationals, or pairs $\{m|n\}$ (on $\mathbb{Z}$ or $\mathbb{D}$). As an application, we establish that every position in \textsc{Yashima} game on bipartite graphs has an integer pair value. |
| title | Various Diamond Properties in Combinatorial Game Theory |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.21744 |