English

3 dimensional Wythoff Nim

Combinatorics 2024-12-25 v3 Dynamical Systems Number Theory

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.

Keywords

Cite

@article{arxiv.2412.08399,
  title  = {3 dimensional Wythoff Nim},
  author = {Shigeki Akiyama},
  journal= {arXiv preprint arXiv:2412.08399},
  year   = {2024}
}

Comments

Minor revision. Welcome comments and information on missing references

R2 v1 2026-06-28T20:30:58.906Z