Row Impartial Terminus
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908517834686464 |
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| author | Gottlieb, Eric Khatana, Dawood Krnc, Matjaž Muršič, Peter Qureshi, Ismael |
| author_facet | Gottlieb, Eric Khatana, Dawood Krnc, Matjaž Muršič, Peter Qureshi, Ismael |
| contents | We introduce Row Impartial Terminus (RIT), an impartial combinatorial game played on integer partitions. We show that any position in RIT can be uniquely decomposed into a core and a remnant. Our central result is that the Conway pair of any RIT position-which determines the outcome under both normal and misère play-is identical to the Conway pair of a corresponding position in the game of Nim defined by the remnant. This finding provides a complete winning strategy for both variants of RIT, reducing its analysis to the well-understood framework of Nim. As a consequence, we classify RIT within the Conway-Gurvich-Ho hierarchy, showing it to be forced and miserable but not pet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Row Impartial Terminus Gottlieb, Eric Khatana, Dawood Krnc, Matjaž Muršič, Peter Qureshi, Ismael Combinatorics Discrete Mathematics We introduce Row Impartial Terminus (RIT), an impartial combinatorial game played on integer partitions. We show that any position in RIT can be uniquely decomposed into a core and a remnant. Our central result is that the Conway pair of any RIT position-which determines the outcome under both normal and misère play-is identical to the Conway pair of a corresponding position in the game of Nim defined by the remnant. This finding provides a complete winning strategy for both variants of RIT, reducing its analysis to the well-understood framework of Nim. As a consequence, we classify RIT within the Conway-Gurvich-Ho hierarchy, showing it to be forced and miserable but not pet. |
| title | Row Impartial Terminus |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2509.03390 |