Mis\`ere canonical forms of partizan games
Combinatorics
2007-05-23 v1
Abstract
We show that partizan games admit canonical forms in mis\`ere play. The proof is a synthesis of the canonical form theorems for normal-play partizan games and mis\`ere-play impartial games. It is fully constructive, and algorithms readily emerge for comparing mis\`ere games and calculating their canonical forms. We use these techniques to show that there are precisely 256 games born by day 2, and to obtain a bound on the number of games born by day 3.
Cite
@article{arxiv.math/0703565,
title = {Mis\`ere canonical forms of partizan games},
author = {Aaron N. Siegel},
journal= {arXiv preprint arXiv:math/0703565},
year = {2007}
}
Comments
12 pages