A030129 Number of nonisomorphic Steiner triple systems (STS's) S(2,3,n) on n points.

1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 80, 0, 0, 0, 11084874829, 0, 14796207517873771

Offset

1,13

Comments

a(n) also counts the following objects:

isomorphism classes of idempotent totally symmetric Latin squares of order n,

isotopism classes containing idempotent totally symmetric Latin squares of order n,

species containing idempotent totally symmetric Latin squares of order n,

isomorphism classes of totally symmetric loops of order n+1,

isomorphism classes of totally symmetric unipotent Latin squares of order n+1,

isomorphism classes containing totally symmetric reduced Latin squares of order n+1,

isotopism classes containing totally symmetric unipotent Latin squares of order n+1,

isotopism classes containing totally symmetric reduced Latin squares of order n+1,

species containing totally symmetric unipotent Latin squares of order n+1, and

species containing totally symmetric reduced Latin squares of order n+1.

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 304.

CRC Handbook of Combinatorial Designs, 1996, p. 70.

Links

Table of n, a(n) for n=1..21.

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.

Crossrefs

Cf. A001201, A030128, A051390, A124118, A124119, A076019.

Sequence in context: A098276 A335692 A215880 * A012647 A012334 A012451

Adjacent sequences: A030126 A030127 A030128 * A030130 A030131 A030132

Keyword

nonn,nice,hard,more

Author

Eric W. Weisstein

Status

approved