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
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.
CROSSREFS
KEYWORD
nonn,nice,hard,more
AUTHOR
STATUS
approved