Misere quotients for impartial games
Thane Plambeck, Aaron N. Siegel · arXiv (Cornell University) · 2006
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also introduce several advances in the structure theory of misere quotients, including a connection between the combinatorial structure of normal and misere play.