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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
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OFFSET
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2,2
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COMMENTS
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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.
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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 Jeffrey H. Dinitz and D. R. Stinson, editors, Contemporary Design Theory, Wiley, 1992.
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LINKS
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EXAMPLE
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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
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Triangle in A066701 gives number of nonisomorphic solutions.
Triangle in A036838 (the Schoenheim bound) gives lower bounds to these entries.
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KEYWORD
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AUTHOR
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STATUS
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approved
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