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