A066010 - OEIS

%I #14 Feb 02 2020 20:50:52

%S 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,

%T 30,30,16,8,1,5,17,30,51,50,45,20,9,1,6,19,47,66

%N Triangle of covering numbers T(n,k) = C(n,k,k-1), n >= 2, 2 <= k <= n.

%C 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.

%D CRC Handbook of Combinatorial Designs, 1996, p. 263.

%D 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.

%H D. Applegate, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205303">On asymmetric coverings and covering numbers</a>, J. Comb. Des. 11 (2003), 218-228.

%H D. Gordon, <a href="http://www.dmgordon.org/cover">La Jolla Repository of Coverings</a>

%H K. J. Nurmela and Patric R. J. Östergård, <a href="http://www.tcs.hut.fi/old/papers/tp1.ps.Z">New coverings of t-sets with (t+1)-sets</a>, J. Combinat. Designs, 7 (1999), 217-226.

%H K. J. Nurmela and Patric R. J. Östergård, <a href="http://www.tcs.hut.fi/old/papers/table3.html">New coverings of t-sets with (t+1)-sets (appendix)</a>, J. Combinat. Designs, 7 (1999), 217-226.

%H <a href="/index/Cor#covnum">Index entries for covering numbers</a>

%e Table of values of C(v,k,k-1):

%e v\k.2..3..4...5...6...7...8..9.10.11.12.13

%e .2 .1

%e .3 .2..1

%e .4 .2..3..1

%e .5 .3..4..4...1

%e .6 .3..6..6...5...1

%e .7 .4..7.12...9...6...1

%e .8 .4.11.14..20..12...7...1

%e .9 .5.12.25..30..30..16...8..1

%e 10 .5.17.30..51..50..45..20..9..1

%e 11 .6.19.47..66...a..84..63.25.10..1

%e 12 .6.24.57.113.132...b.126.84.30.11..1

%e 13 .7.26.78.???.245.???..?.185.??.36.12.1

%e where a in range 96-100, b in range 165-176

%Y Columns give A011975, A011979, A011983, A011987, A066009, A066011, A066137, A066140, A066225.

%Y Triangle in A066701 gives number of nonisomorphic solutions.

%Y Triangle in A036838 (the Schoenheim bound) gives lower bounds to these entries.

%K nonn,tabl,nice

%O 2,2

%A _N. J. A. Sloane_, Dec 30 2001