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Search: id:A066701
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| A066701 |
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Triangle giving number of nonisomorphic minimal covering designs with parameters (n, k, k-1) (designs achieving the covering number C(n,k,k-1) given in A066010), for n >= 2, 2 <= k <= n. |
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2
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 6, 1, 1, 1, 1, 1, 77, 3, 2, 1, 1, 1, 1, 58, 1, 40, 1, 20, 1, 1, 1, 1, 2
(list; table; graph; listen)
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OFFSET
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2,18
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COMMENT
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C(v,k,t) is the smallest number of k-subsets of an n-set such that every t-subset is contained in at least one of the k-subsets. This sequence says how many different solutions there are for C(n,k,k-1).
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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 263.
W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of J. H. Dinitz and D. R. Stinson, editors,a Contemporary Design Theory, Wiley, 1992.
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LINKS
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D. Applegate, E. M. Rains and N. J. A. Sloane, On asymmetric coverings and covering numbers, J. Comb. Des. 11 (2003), 218-228.
D. Gordon, La Jolla Repository of Coverings
K. J. Nurmela and P. R. J. Ostergard, New coverings of t-sets with (t+1)-sets, J. Combinat. Designs, 7 (1999), 217-226.
K. J. Nurmela and P. R. J. Ostergard, New coverings of t-sets with (t+1)-sets (appendix), J. Combinat. Designs, 7 (1999), 217-226.
Index entries for covering numbers
Index entries for sequences related to Steiner systems
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CROSSREFS
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Cf. A066010. A030129 gives entries in second column in the cases when a Steiner triple system exists.
A051390 gives entries in 3rd column in the cases when a Steiner quadruple system exists.
Adjacent sequences: A066698 A066699 A066700 this_sequence A066702 A066703 A066704
Sequence in context: A046592 A010326 A053231 this_sequence A046563 A046591 A119350
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KEYWORD
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nonn,nice,tabl
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AUTHOR
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njas, Jan 11 2002
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