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%I #11 Jul 08 2014 11:05:35
%S 1,0,1,1,1,6,9,50,211
%N Number of misere quotients of order 2n.
%C 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." [Quotation corrected by Thane Plambeck, Jul 08 2014]
%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see pp. 89 and 102.
%D J. H. Conway, On Numbers and Games, Second Edition. A. K. Peters, Ltd, 2001, p. 128.
%D T. E. Plambeck, Advances in Losing, in M. Albert and M. J. Nowakowski, eds., Games of No Chance 3, Cambridge University Press, forthcoming.
%H Achim Flammenkamp, <a href="http://www.uni-bielefeld.de/~achim/octal_sparse.html">Sparse- and Common-Positions of Sprague-Grundy Values of Octal-Games</a>
%H Aaron N. Siegel, <a href="http://arXiv.org/abs/math.CO/0703070">The structure and classification of misere quotients</a>, figure 1, p. 3, 2 Mar 2007.
%Y Cf. A071074, A071434.
%K nonn,hard
%O 1,6
%A _Jonathan Vos Post_, Mar 05 2007
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