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Misere quotients for impartial games

Thane E. Plambeck·Aaron N. Siegel
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Abstract

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.

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Thane E. Plambeck, Aaron N. Siegel. 2007-08-14. Misere quotients for impartial games. https://arxiv.org/abs/math/0609825

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