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COMMENTS
| Siegel's abstract: "A bipartite monoid is a commutative monoid Q together with an identified subset P subset of Q. In this paper we study a class of bipartite monoids, known as misere quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misere quotients with |P| = 2 and give a complete classification of all such quotients up to isomorphism. One consequence is that if |P| = 2 and Q is finite, then |Q| = 2^n+2 or 2^n+4. We then develop computational techniques for enumerating misere quotients of small order and apply them to count the number of non-isomorphic quotients of order at most 18. We also include a manual proof that there is exactly one quotient of order <=8."
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REFERENCES
| E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see pp. 89 and 102.
J. H. Conway, On Numbers and Games, Second Edition. A. K. Peters, Ltd, 2001, p. 128.
T. E. Plambeck, Advances in Losing, in M. Albert and M. J. Nowakowski, eds., Games of No Chance 3, Cambridge University Press, forthcoming.
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