Misere quotients for impartial games
Combinatorics
2008-06-30 v5 Commutative Algebra
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.
Cite
@article{arxiv.math/0609825,
title = {Misere quotients for impartial games},
author = {Thane E. Plambeck and Aaron N. Siegel},
journal= {arXiv preprint arXiv:math/0609825},
year = {2008}
}
Comments
Paper has been split into two parts: this part, and a supplement at arXiv:0705.2404v1