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$ 284\,457$ Steiner triple systems of order $ 19$ contain a subsystem of order $ 9$

Authors: D. R. Stinson and E. Seah
Journal: Math. Comp. 46 (1986), 717-729
MSC: Primary 05B07; Secondary 20B25
MathSciNet review: 829642
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Abstract: In this paper, we enumerate the (nonisomorphic) Steiner triple systems of order 19 which contain a subsystem of order 9. The number of these designs is precisely 284457. We also determine which of these designs also contain at least one subsystem of order 7, and how many. Exactly 13529 of them contain at least one subsystem of order 7.

References [Enhancements On Off] (What's this?)

  • [1] R. Déherder, Recouvrements, Thèse de doctorat, Université Libre de Bruxelles, 1976.
  • [2] E. N. Gelling, On One-Factorizations of the Complete Graph and the Relationship to Round Robin Schedules, M. Sc. Thesis, University of Victoria, 1973.
  • [3] E. S. Kramer & D. M. Mesner, "Intersections among Steiner systems," J. Combin. Theory, v. 16, 1974, pp. 273-285. MR 0335296 (49:78)
  • [4] R. A. Mathon, K. T. Phelps & A. Rosa, "Small Steiner triple systems and their properties," Ars Combin., v. 15, 1983, pp. 3-110. MR 706292 (85e:05027a)
  • [5] D. R. Stinson & H. Ferch, "2000000 Steiner triple systems of order 19," Math. Comp., v. 44, 1985, pp. 533-535. MR 777284 (86e:05014)

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Article copyright: © Copyright 1986 American Mathematical Society

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