Equality Classes of Nim Positions under Mis\`ere Play
Combinatorics
2016-07-25 v2
Abstract
We determine the mis\`{e}re equivalence classes of Nim positions under two equivalence relations: one based on playing disjunctive sums with other impartial games, and one allowing sums with partizan games. In the impartial context, the only identifications we can make are those stemming from the known fact about adding a heap of size 1. In the partizan context, distinct Nim positions are inequivalent.
Cite
@article{arxiv.1506.02261,
title = {Equality Classes of Nim Positions under Mis\`ere Play},
author = {Mark Spindler},
journal= {arXiv preprint arXiv:1506.02261},
year = {2016}
}
Comments
10 pages, LaTeX; fixed typos, improved formatting consistency, added section on transfinite Nim