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Combinatorial Games (II) -Different Moves for Left and Right

Feature Column Archive

7. References

Some of the references, but not all of them, from my column on impartial games also appear below. A bibliography devoted to hex can be found on line.

Berlekamp, E., The hackenbush number system for compression of numerical data, Information and Control 26 (1974) 134-140.

Berlekamp, E., Two-person, perfect information games, in The Legacy of John von Neumann, Proc. Symposium in Pure Mathematics, Volume 50, American Mathematical Society, 1990, p. 275-287.

Berlekamp, E. and D. Wolfe, Mathematical Go - Chilling gets the last point, A. K. Peters, Wellesley, 1994.

Browne, C., Hex strategy: making the right connections, A. K. Peters, Wellesley, 2001.

Bruno, J., and Weinberg, L. A constructive graph-theoretic solution of the Shannon Switching Game. IEEE Trans. Circuit Theory CT-17, 1 (Feb. 1970), 74-81.

Conway, J., On Numbers and Games, Academic Press, New York, 1976.

Conway, J. On Numbers and Games, second edition, A.K. Peters, 2001.

Conway, J., All games bright and beautiful, Amer. Math. Monthly 84 (1977) 417-434.

Berlekamp, E., and J. Conway, R. Guy, Winning Ways, Academic Press, London, 1982 (Second Edition, in more volumes, by A. K. Peters).

Gonshor, H., An Introduction to the Theory of Surreal Numbers, London Mathematical Society, Lecture Notes Series, Volume 110, Cambridge U. Press, Cambridge, 1986.

Guy, R. Combinatorial Games, in Handbook of Combinatorics, R. Graham, and M. Grotschel, and L. Lovasz, (eds.), Vol. II, North-Holland, Amsterdam, 1996, p. 2117-2162.

Guy, R., (ed.), Combinatorial Games, Volume 43, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence, 1991.

Guy, R. and R. Woodrow, (ed.), The Lighter Side of Mathematics, Mathematical Association of America, Washington, 1994.

Knuth, D., Surreal Numbers, Addison-Wesley, Reading, 1974.

Lehman, A. A solution to the Shannon Switching Game. SIAM J. 12, No. 4 (Dec. 1964), 687-725.

Louck, J., Conway numbers and iteration theory, Adv. Appl. Math., 2 (1997) 181-215.

Nowakowski, R., (ed.), Games of No Chance, Cambridge U. Press, New York, 1996.

Nowakowski, R., (ed.), More Games of No Chance, Cambridge U. Press, New York, 2003.

Schleicher, D. and M. Stoll, An introduction to Conway's games and numbers, (preprint: 2002).

Shaki, A., Algebraic solutions of partizan games with cycles, Math. Proc. Camb. Phil. Soc. 85 (1979) 227-246.

Singmaster, D., Almost all partizan games are first person and almost all impartial games are maximal, J. Combin. Inform. System Sci. 7 (1982) 270--274.

Note 1: Many examples of combinatorial games can be found in the books and articles of Martin Gardner.

Note 2: Those who can access JSTOR can find some of the papers mentioned above there.

  1. Introduction
  2. Hex
  3. Hackenbush
  4. Counting and sets
  5. Surreal numbers
  6. Surreal numbers and games
  7. References