Bulletin of the American Mathematical Society

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Book Information:

Author: J. H. Conway
Title: On numbers and games
Additional book information: Academic Press, London, New York, San Francisco, 1976, ix + 238 pp., $26.50.

Author: D. E. Knuth
Title: Surreal numbers
Additional book information: Addison-Wesley, Reading, Massachusetts, 1976, 119 pp.

Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Second printing. MR 0413592

E. R. Berlekamp, The Hackenbush number system for compression of numerical data, Information and Control 26 (1974), 134–140. MR 354140

3.

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning ways, a book estimated to appear in 1978.

4.

J. H. Conway, All numbers great and small, Univ. of Calgary Math. Res. Paper #149, 1972.

J. H. Conway, All games bright and beautiful, Amer. Math. Monthly 84 (1977), no. 6, 417–434. MR 446534, DOI 10.2307/2321899

A. S. Fraenkel and Y. Perl, Constructions in combinatorial games with cycles, Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. II, Colloq. Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975, pp. 667–699. MR 0384171

A. S. Fraenkel and Y. Yesha, Theory of annihilation games, Bull. Amer. Math. Soc. 82 (1976), no. 5, 775–777. MR 449726, DOI 10.1090/S0002-9904-1976-14160-2

Aviezri S. Fraenkel and Yaacov Yesha, The generalized Sprague-Grundy function and its invariance under certain mappings, J. Combin. Theory Ser. A 43 (1986), no. 2, 165–177. MR 867643, DOI 10.1016/0097-3165(86)90058-0

A. S. Fraenkel and Y. Yesha, Complexity of problems in games, graphs and algebraic equations, Discrete Appl. Math. 1 (1979), no. 1-2, 15–30. MR 544387, DOI 10.1016/0166-218X(79)90012-X

10.

M. Gardner, Mathematical games, a column in Scientific American.

Richard K. Guy, Combinatorial games, Handbook of combinatorics, Vol. 1, 2, Elsevier Sci. B. V., Amsterdam, 1995, pp. 2117–2162. MR 1373699

Richard K. Guy and Cedric A. B. Smith, The $G$-values of various games, Proc. Cambridge Philos. Soc. 52 (1956), 514–526. MR 82408

Shuo Yen R. Li, Sums of Zuchswang games, J. Combinatorial Theory Ser. A 21 (1976), no. 1, 52–67. MR 426869, DOI 10.1016/0097-3165(76)90046-7

Edward M. Reingold, Jurg Nievergelt, and Narsingh Deo, Combinatorial algorithms: theory and practice, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1977. MR 0471431

Cedric A. B. Smith, Graphs and composite games, J. Combinatorial Theory 1 (1966), 51–81. MR 194362

Thomas J. Schaefer, Complexity of decision problems based on finite two-person perfect-information games, Eighth Annual ACM Symposium on Theory of Computing (Hershey, Pa., 1976), Assoc. Comput. Mach., New York, 1976, pp. 41–49. MR 0451853

C. P. Welter, The theory of a class of games on a sequence of squares, in terms of the advancing operation in a special group, Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indagationes Math. 16 (1954), 194–200. MR 0060512

1.

A. V. Aho, J. E. Hopcroft and J. D. Ullman, The design and analysis of computer algorithms, Addison-Weslcy, Reading, Mass., 1974. MR 0413592

2.

E. R. Berlekamp, The Hackenbush number system for compression of numerical data. Information and Control 26 (1974), 134-140. MR 354140

3.

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning ways, a book estimated to appear in 1978.

4.

J. H. Conway, All numbers great and small, Univ. of Calgary Math. Res. Paper #149, 1972.

5.

J. H. Conway, All games bright and beautiful, Amer. Math. Monthly 84 (1977), 417-434. (Essentially the same as Univ. of Calgary Math. Res. Paper #295, 1975, which has the same title.) MR 446534

6.

A. S. Fraenkel and Y. Perl, Constructions in combinatorial games with cycles, Colloquia Mathematica Societatis János Bolyai 10: Proc. International Colloquium on Infinite and Finite Sets, Keszthely, Hungary, 1973 (A. Hajnal, R. Rado, V. T. Sós, eds.), Vol. 2, North-Holland, Amsterdam, 1975, pp. 667-699. MR 384171

7.

A. S. Fraenkel and Y. Yesha, Theory of annihilation games, Bull. Amer. Math. Soc. 82 (1976), 775-777. MR 449726

8.

A. S. Fraenkel and Y. Yesha, The generalized Sprague-Grundy function and its invariance under certain mappings (to appear). MR 867643

9.

A. S. Fraenkel and Y. Yesha, Complexity of problems in games, graphs and algebraic equations (to appear). MR 544387

10.

M. Gardner, Mathematical games, a column in Scientific American.

11.

R. K. Guy, Partizan and impartial combinatorial games, Univ. of Calgary Math. Res. Paper #315, 1976. Shortened version to appear in Proc. Colloq. Internat. C.N.R.S., Paris, 1976. MR 1373699

12.

R. K. Guy and C. A. B. Smith, The G-values of various games, Proc. Cambridge Philos. Soc. 52 (1956), 514-526. MR 82408

13.

S.-Y. R. Li, Sums of Zuchswang games, J. Combinatorial Theory Ser. A 21 (1976), 52-67. MR 426869

14.

E. M. Reingold, J. Nievergelt and N. Deo, Combinatorial algorithms: Theory and practice, Prentice-Hall, Englewood Cliffs, N. J., 1977. MR 471431

15.

C. A. B. Smith, Graphs and composite games, J. Combinatorial Theory 1 (1966), 51-81. MR 194362

16.

T. J. Schaefer, Complexity of decision problems based on finite two-person perfect-information games, Eighth Annual ACM Symposium on Theory of Computing (Hershey, Pa., 1976), pp. 41-49, Assoc, Comput. Mach., New York, 1976. MR 451853

17.

C. P. Welter, The theory of a class of games on a sequence of squares, in terms of the advancing operation in a special group, Nederl. Akad. Wetensch. Proc. Ser. A 57 = Indag. Math. 16 (1954), 194-200. MR 60512