A066009 -id:A066009 - cp's OEIS frontend

A066010 Triangle of covering numbers T(n,k) = C(n,k,k-1), n >= 2, 2 <= k <= n.

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

Offset: 2

N. J. A. Sloane, Dec 30 2001

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.

			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

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.

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 Patric R. J. Östergård, New coverings of t-sets with (t+1)-sets, J. Combinat. Designs, 7 (1999), 217-226.
K. J. Nurmela and Patric R. J. Östergård, New coverings of t-sets with (t+1)-sets (appendix), J. Combinat. Designs, 7 (1999), 217-226.
Index entries for covering numbers

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.

A036834 Schoenheim bound L_1(n,7,6).

Original entry on oeis.org

1, 7, 16, 39, 70, 158, 246, 490, 746, 1253, 1768, 2893, 3876, 5963, 7872, 11308, 14421, 20359, 25300, 34621, 42622, 56160, 67860, 88513, 105201, 134629, 159004, 198862, 231880, 287851, 332112, 407105, 467677, 564018, 642377

Offset: 7

N. J. A. Sloane, Jan 11 2002

nonn

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. See Eq. 1.

Index entries for covering numbers

Lower bound to A066009.

A column of A036838.

A011983 Covering numbers C(n,5,4).

Original entry on oeis.org

1, 5, 9, 20, 30, 51, 66, 113

Offset: 5

N. J. A. Sloane

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.

CRC Handbook of Combinatorial Designs, 1996, p. 263.
D. De Caen, D. L. Kreher, S. P. Radziszowski, and W. H. Mills, On the covering of t-sets with (t+1)-sets: C(9,5,4) and C(10,6,5). Discrete Math. 92 (1991), no. 1-3, 65-77.
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.

D. Applegate, E. M. Rains and N. J. A. Sloane, On asymmetric coverings and covering numbers, arXiv:math/0205303 [math.CO], 2002; J. Comb. Des. 11 (2003), 218-228.
D. Gordon, La Jolla Repository of Coverings
K. J. Nurmela and Patric R. J. Östergård, New coverings of t-sets with (t+1)-sets, J. Combinat. Designs, 7 (1999), 217-226.
K. J. Nurmela and Patric R. J. Östergård, New coverings of t-sets with (t+1)-sets (appendix), J. Combinat. Designs, 7 (1999), 217-226.
Index entries for covering numbers

Cf. A066009. A column of A066010.

Next term is <= 157.

cp's OEIS Frontend

A066010 Triangle of covering numbers T(n,k) = C(n,k,k-1), n >= 2, 2 <= k <= n.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

A036834 Schoenheim bound L_1(n,7,6).

Views

Author

Keywords

References

Links

Crossrefs

A011983 Covering numbers C(n,5,4).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions