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A066010
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Triangle of covering numbers T(n,k) = C(n,k,k-1), n >= 2, 2 <= k <= n.
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10
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1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 6, 6, 5, 1, 4, 7, 12, 9, 6, 1, 4, 11, 14, 20, 12, 7, 1, 5, 12, 25, 30, 30, 16, 8, 1, 5, 17, 30, 51, 50, 45, 20, 9, 1, 6, 19, 47, 66
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| 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.
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REFERENCES
| 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
| 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
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EXAMPLE
| Table of values of C(v,k,k-1):
v\k.2..3..4...5...6...7...8..9.10.11.12.13
.2 .1
.3 .2..1
.4 .2..3..1
.5 .3..4..4...1
.6 .3..6..6...5...1
.7 .4..7.12...9...6...1
.8 .4.11.14..20..12...7...1
.9 .5.12.25..30..30..16...8..1
10 .5.17.30..51..50..45..20..9..1
11 .6.19.47..66...a..84..63.25.10..1
12 .6.24.57.113.132...b.126.84.30.11..1
13 .7.26.78.???.245.???..?.185.??.36.12.1
where a in range 96-100, b in range 165-176
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CROSSREFS
| Columns give A011975, A011979, A011983, A011987, A066009, A066011, A066137, A066140, A066225.
Triangle in A066701 gives number of nonisomorphic solutions.
Triangle in A036838 (the Schoenheim bound) gives lower bounds to these entries.
Sequence in context: A103627 A080786 A036838 * A109974 A026820 A091438
Adjacent sequences: A066007 A066008 A066009 * A066011 A066012 A066013
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2001
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