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Search: id:A137348
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| A137348 |
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Number of Steiner quadruple systems (SQS's) of order n. |
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+0
1
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| 1, 1, 0, 1, 0, 0, 0, 30, 0, 2520, 0, 0, 0, 37362124800, 0, 14311959985625702400, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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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 "P. Kaski, P. R. J. Ostergard (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16". SQS(20) is still unknown.
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REFERENCES
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P. Kaski, P. R. J. Ostergard (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
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LINKS
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Vesa Linja-aho, Home Page.
Vesa Linja-aho, Python program
Index entries for sequences related to Steiner systems
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EXAMPLE
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There are 2520 SQS's on 10 points.
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CROSSREFS
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Adjacent sequences: A137345 A137346 A137347 this_sequence A137349 A137350 A137351
Sequence in context: A023926 A022068 A030128 this_sequence A137737 A062513 A040906
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KEYWORD
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hard,nonn
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AUTHOR
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Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 08 2008, May 13 2008
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