Misere quotients for impartial games

Details Misere quotients for impartial games Misere quotients for impartial games

2006-09-28

arxiv.org/abs/math/0609825v5

Journal of Combinatorial Theory, Series A (May 2008) pp 593-622

Mathematics

Combinatorics

Paper has been split into two parts: this part, and a supplement at arXiv:0705.2404v1

Scientific paper

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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