Mind the gap: A real-valued distance on combinatorial games
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915732800929792 |
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| author | Burke, Kyle Fisher, Michael Tennenhouse, Craig |
| author_facet | Burke, Kyle Fisher, Michael Tennenhouse, Craig |
| contents | We define a real-valued distance metric $wd$ on the space $\mathcal{C}$ of short combinatorial games in canonical form. We demonstrate the existence of Cauchy sequences informed by sidling sequences, find limit points, and investigate the closure $\overline{\mathcal{C}}$, which is shown to partition the set of loopy games in a non-trivial way. Stoppers, enders, and non-stopper-sided loopy games are explored, as well as the topological properties of $(\mathcal{C},wd)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mind the gap: A real-valued distance on combinatorial games Burke, Kyle Fisher, Michael Tennenhouse, Craig Combinatorics 91A46 G.2.1 We define a real-valued distance metric $wd$ on the space $\mathcal{C}$ of short combinatorial games in canonical form. We demonstrate the existence of Cauchy sequences informed by sidling sequences, find limit points, and investigate the closure $\overline{\mathcal{C}}$, which is shown to partition the set of loopy games in a non-trivial way. Stoppers, enders, and non-stopper-sided loopy games are explored, as well as the topological properties of $(\mathcal{C},wd)$. |
| title | Mind the gap: A real-valued distance on combinatorial games |
| topic | Combinatorics 91A46 G.2.1 |
| url | https://arxiv.org/abs/2601.10574 |