Isomorphism Theorems for Impartial Combinatorial Games
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908605152755712 |
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| author | Baltushkin, Mikhail Ernst, Dana C. Sieben, Nándor |
| author_facet | Baltushkin, Mikhail Ernst, Dana C. Sieben, Nándor |
| contents | We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four isomorphism theorems from universal algebra are valid in this category. Quotient optiongraphs, including the minimum quotient, provide simplifications that can help in the analysis of games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphism Theorems for Impartial Combinatorial Games Baltushkin, Mikhail Ernst, Dana C. Sieben, Nándor Combinatorics 91A46, 91A43, 05C57, 08A30 We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four isomorphism theorems from universal algebra are valid in this category. Quotient optiongraphs, including the minimum quotient, provide simplifications that can help in the analysis of games. |
| title | Isomorphism Theorems for Impartial Combinatorial Games |
| topic | Combinatorics 91A46, 91A43, 05C57, 08A30 |
| url | https://arxiv.org/abs/2505.04919 |