A030129
Number of nonisomorphic Steiner triple systems (STS's) S(2,3,n) on n points.
Original entry on oeis.org
1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 80, 0, 0, 0, 11084874829, 0, 14796207517873771
Offset: 1
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 304.
- CRC Handbook of Combinatorial Designs, 1996, p. 70.
- Daniel Heinlein and Patric R. J. Östergård, Enumerating Steiner Triple Systems, arXiv:2303.01207 [math.CO], 2023.
- Petteri Kaski and Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi), The Steiner triple systems of order 19.
- Petteri Kaski and Patric R. J. Östergård, The Steiner triple systems of order 19, Mathematics of Computation, Vol. 73, No. 248 (Oct., 2004), pp. 2075-2092.
- Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.
- Eric Weisstein's World of Mathematics, Steiner Triple System.
- Index entries for sequences related to Steiner systems.
A051390
Number of nonisomorphic Steiner quadruple systems (SQS's) of order n.
Original entry on oeis.org
1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1054163
Offset: 1
There are 4 nonisomorphic SQS's on 14 points.
- CRC Handbook of Combinatorial Designs, 1996, circa p. 70.
- A. Hartman and K. T. Phelps, Steiner quadruple systems, pp. 205-240 of Contemporary Design Theory, ed. Jeffrey H. Dinitz and D. R. Stinson, Wiley, 1992.
- Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16, Journal of Combinatorial Theory, Series A, Volume 113, Issue 8, November 2006, Pages 1764-1770.
- V. A. Zinoviev and D. V. Zinoviev, Classification of Steiner Quadruple Systems of order 16 and rank 14, [English translation from Russian], Problemy Peredachi Informatsii, 42 (No. 3, 2006), 59-72.
- V. A. Zinoviev and D. V. Zinoviev, Classification of Steiner Quadruple Systems of order 16 and rank 14, Problems of Information Transmission, July-September 2006, Volume 42, Issue 3, pp 217-229; from [in Russian], Problemy Peredachi Informatsii, 42 (No. 3, 2006), 59-72.
- Index entries for sequences related to Steiner systems
See
A124120,
A124119 for other versions of this sequence. The present entry is the official version.
A124120
Number of nonisomorphic Steiner quadruple systems (SQS's) S(3,4,n) on n points.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1054163
Offset: 1
There are 4 nonisomorphic SQS's on 14 points.
A051390 is the official version of this sequence and has all the references etc.
A051391
Number of nonisomorphic Steiner triple systems (STS's) S(2,3,v) on v = 6n+1 or 6n+3 points.
Original entry on oeis.org
1, 1, 1, 1, 2, 80, 11084874829
Offset: 1
There are 2 nonisomorphic STS's on 13 points.
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 304.
- CRC Handbook of Combinatorial Designs, 1996, p. 70.
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