English

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.

Keywords

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}
}

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12 pages