Two Dimensional Subtraction -- Transfer Games
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917521677877248 |
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| author | Danai, Alon Ellis, Paul Thanatipanonda, Thotsaporn Aek |
| author_facet | Danai, Alon Ellis, Paul Thanatipanonda, Thotsaporn Aek |
| contents | We generalize the results and conjectures of Tamás Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of tokens, where players alternate either taking some tokens from a pile or transferring tokens from one pile to the other. In many cases, we calculate the exact period. We also develop several new notions of periodicitiy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14325 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two Dimensional Subtraction -- Transfer Games Danai, Alon Ellis, Paul Thanatipanonda, Thotsaporn Aek Combinatorics We generalize the results and conjectures of Tamás Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of tokens, where players alternate either taking some tokens from a pile or transferring tokens from one pile to the other. In many cases, we calculate the exact period. We also develop several new notions of periodicitiy. |
| title | Two Dimensional Subtraction -- Transfer Games |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.14325 |