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arXiv · 2412.08399

3 dimensional Wythoff Nim

Shigeki Akiyama
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Abstract

We introduce a new generalization of Wythoff Nim using three piles of stones. We show that its P-positions have finite difference properties and produce a partition of positive integers. Further, we give a conjecture that the P-positions approximate a half-line whose slope is described by algebraic numbers of degree 5.

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Shigeki Akiyama. 2024-12-24. 3 dimensional Wythoff Nim. https://arxiv.org/abs/2412.08399

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