Steiner triple systems of order contain a subsystem of order

Authors:
D. R. Stinson and E. Seah

Journal:
Math. Comp. **46** (1986), 717-729

MSC:
Primary 05B07; Secondary 20B25

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829642-7

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.

**[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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DOI:
https://doi.org/10.1090/S0025-5718-1986-0829642-7

Article copyright:
© Copyright 1986
American Mathematical Society