On the structure of misère impartial games. (English) Zbl 1490.91044
Summary: We consider the abstract structure of the monoid \(\mathcal{M}\) of misère impartial game values. Several new results are presented, including a proof that the group of fractions of \(\mathcal{M}\) is almost torsion-free; a method of calculating the number of distinct games born by day 7; and some new results on the structure of prime games. Also included are proofs of a few older results due to Conway, such as the cancellation theorem, that are essential to the analysis but whose proofs are not readily available in the literature.
MSC:
| 91A46 | Combinatorial games |
References:
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