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arXiv · 2602.14325

Two Dimensional Subtraction -- Transfer Games

Alon Danai·Paul Ellis·Thotsaporn Aek Thanatipanonda
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Abstract

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.

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Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda. 2026-05-22. Two Dimensional Subtraction -- Transfer Games. https://arxiv.org/abs/2602.14325

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