Steiner triple systems of order
Authors:
D. R. Stinson and H. Ferch
Journal:
Math. Comp. 44 (1985), 533535
MSC:
Primary 05B07
MathSciNet review:
777284
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Abstract 
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Abstract: Using a hillclimbing algorithm, we construct 2117600 Steiner triple systems of order 19. These are tested for isomorphism by means of invariants, and 2111276 are shown to be nonisomorphic.
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 [2]
 R. Deherder, Recouvrements, Thesis, Université Libre de Bruxelles, 1976, 212 pp.
 [3]
 R. H. F. Denniston, "Nonisomorphic reverse Steiner triple systems of order 19," Ann. Discrete Math., v. 7, 1980, pp. 255264. MR 584416
 [4]
 T. P. Kirkman, "On a problem in combinations," Cambridge and Dublin Math. J., v. 2, 1847, 191204.
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 K. T. Phelps & A. Rosa, "Rotational Steiner triple systems," Discrete Math., v. 33, 1981, pp. 5766. MR 597228 (82a:05018)
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 A. R. Prince, "Steiner triple systems of order 19 constructed from the Steiner triple system of order 9," Proc. Roy. Soc. Edinburgh Sect. A., v. 94, 1983, pp. 8992. MR 700503 (84f:05022)
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 R. W. Quackenbush, "Algebraic speculations about Steiner systems," Ann. Discrete Math., v. 7, 1980, pp. 2535. MR 584401
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 G. A. F. Seber, "The Estimation of Animal Abundance and Related Parameters, Griffin, London and High Wycombe, 1982. MR 686755 (84k:92001)
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 D. R. Stinson, "Hillclimbing algorithms for the construction of combinatorial designs," Ann. Discrete Math. (To appear.) MR 833797 (87f:05033)
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 D. R. Stinson "A comparison of two invariants for Steiner triple systems: fragments and trains," Ars Combin., v. 16, 1983, pp. 6976. MR 734047 (85f:05023)
 [11]
 D. R. Stinson & E. Seah, "284457 Steiner triple systems of order 19 contain a subsystem of order 9." (Preprint)
 [12]
 R. M. Wilson, "Nonisomorphic Steiner triple systems," Math. Z., v. 135, 1974, pp. 303313. MR 0340046 (49:4803)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198507772843
PII:
S 00255718(1985)07772843
Article copyright:
© Copyright 1985
American Mathematical Society
