|
|
A137348
|
|
Number of Steiner quadruple systems (SQS's) of order n.
|
|
1
|
|
|
1, 1, 0, 1, 0, 0, 0, 30, 0, 2520, 0, 0, 0, 37362124800, 0, 14311959985625702400, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
The values are calculated by utilizing the Knuth's Algorithm X. Only the number of non-isomorphic SQS's is presented in peer-reviewed literature and scientific textbooks. The algorithm was verified to be valid by seeking STS's presented in A001201.
n=14 calculated from "Mendelsohn and Hung: On Steiner Systems S(3,4,14) and S(4,5,15), Util. Math. Vol 1 (1972), pp. 5-95" with orbit-stabilizer theorem
n=15 is given in "Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16". SQS(20) is still unknown.
|
|
REFERENCES
|
Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16
N. S. Mendelsohn and S. H. Y. Hung, On the Steiner Systems S(3,4,14) and S(4,5,15), Util. Math. Vol. 1, 1972, pp. 5-95
|
|
LINKS
|
|
|
EXAMPLE
|
There are 2520 SQS's on 10 points.
|
|
CROSSREFS
|
|
|
KEYWORD
|
hard,nonn
|
|
AUTHOR
|
Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 08 2008, May 13 2008
|
|
STATUS
|
approved
|
|
|
|