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Book Review
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Book Information
Author(s):
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(s):
D. E. Knuth
Title:
Surreal numbers
Additional book information:
Addison-Wesley, Reading, Massachusetts, 1976, 119 pp.
References:
- 1.
- A. V. Aho, J. E. Hopcroft and J. D. Ullman, The design and analysis of computer algorithms, Addison-Weslcy, Reading, Mass., 1974. MR 413592
- 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
Additional Information:
Reviewer(s):
Aviezri S.
Fraenkel
Review Information:
Journal:
Bull. Amer. Math. Soc.
84
(1978),
1328-1336.
DOI:
10.1090/S0002-9904-1978-14564-9
PII:
S 0002-9904(1978)14564-9
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