English

Mixed-Radix Nim

Combinatorics 2019-01-09 v2

Abstract

We present take-away games whose Sprague-Grundy functions are given by the Nim sum of heap sizes in a mixed base β\beta. Let Δβ\Delta_\beta be the set of such games. We give a necessary and sufficient condition for the existence of a minimum of Δβ\Delta_\beta, and a recursive construction of the maximum of Δβ\Delta_\beta.

Keywords

Cite

@article{arxiv.1801.00616,
  title  = {Mixed-Radix Nim},
  author = {Yuki Irie},
  journal= {arXiv preprint arXiv:1801.00616},
  year   = {2019}
}
R2 v1 2026-06-22T23:34:17.812Z