1,6

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."

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.

Achim Flammenkamp, Sparse- and Common-Positions of Sprague-Grundy Values of Octal-Games

Aaron N. Siegel, The structure and classification of misere quotients, figure 1, p. 3, 2 Mar 2007.

Cf. A071074, A071434.

Sequence in context: A004989 A147355 A154139 this_sequence A098662 A056425 A056416

Adjacent sequences: A126107 A126108 A126109 this_sequence A126111 A126112 A126113

nonn,hard

Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 05 2007