publication . Preprint . 2006

Mis\`ere Games and Mis\`ere Quotients

Siegel, Aaron N.;
Open Access English
  • Published: 20 Dec 2006
Comment: 34 pages; fixed references
free text keywords: Mathematics - Combinatorics, Mathematics - Commutative Algebra, 91A46
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18 references, page 1 of 2

[1] C. L. Bouton. Nim, a game with a complete mathematical theory. Ann. of Math., 3(2):35-39, 1902.

[2] J. H. Conway. On Numbers and Games. A. K. Peters, Ltd., Natick, MA, second edition, 2001.

[3] J. H. Conway, D. Hoey, and A. N. Siegel. Forthcoming paper on mis`ere games.

[4] A. Flammenkamp. Sprague-Grundy values of octal games.

[5] P. A. Grillet. Commutative Semigroups. Number 2 in Advances in Mathematics. Springer, 2001.

[6] P. M. Grundy. Mathematics and games. Eureka, 2:6-8, 1939.

[7] P. M. Grundy and C. A. B. Smith. Disjunctive games with the last player losing. Proc. Cambridge Philos. Soc., 52:527-533, 1956.

[8] R. K. Guy and C. A. B. Smith. The G-values of various games. Proc. Cambridge Philos. Soc., 52:514-526, 1956.

[9] T. E. Plambeck. Mis`ere games (web pages devoted to problems, computer software, and theoretical results).

[10] T. E. Plambeck. Taming the wild in impartial combinatorial games. INTEGERS: The Electr. J. Combin. Number Thy., 5(#G05), 2005. [OpenAIRE]

[11] T. E. Plambeck. Advances in losing. In M. Albert and R. J. Nowakowski, editors, Games of No Chance 3, MSRI Publications. Cambridge University Press, Cambridge, forthcoming.

[12] T. E. Plambeck and A. N. Siegel. Mis`ere Games on the Web.

[13] T. E. Plambeck and A. N. Siegel. Mis`ere quotients for impartial games. Forthcoming.

[14] L. R´edei. The Theory of Finitely Generated Commutative Semigroups. Pergamon, 1965.

[15] A. N. Siegel. MisereSolver.

18 references, page 1 of 2
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