A066019 Triangle of covering numbers T(n,k) = C(n,k,k-2), n >= 3, 3 <= k <= n.

1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 3, 5, 5, 5, 1, 3, 6, 8, 7, 6, 1, 3, 8, 12, 12, 9, 7, 1, 4, 9, 17, 20, 20, 12, 8, 1, 4, 11, 20, 32, 34, 29, 15, 9, 1, 4, 12, 29

Offset

3,2

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.

References

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.

Kari J. Nurmela and Patric R. J. Östergård, Covering t-sets with (t+2)-sets. Proceedings of the Conference on Optimal Discrete Structures and Algorithms-ODSA '97 (Rostock).

Links

Table of n, a(n) for n=3..50.

D. Gordon, La Jolla Repository of Coverings

Kari J. Nurmela and Patric R. J. Östergård, Covering t-sets with (t+2)-sets, Discrete Appl. Math. 95 (1999), no. 1-3, 425-437.

Index entries for covering numbers

Example

Triangle begins:
  1;
  2 1;
  2 3 1;
  2 3 4 1;
  3 5 5 5 1;
  ...

Prog

(Sage)
from sage.combinat.designs.covering_design import best_known_covering_design_www
def T(n, k):
  if k==3: return ceil(n/3)
  if k==n: return 1
  C = best_known_covering_design_www(n, k, k-2)
  assert C.size() == C.low_bd()
  return C.size()
# Max Alekseyev, Feb 14 2025

Crossrefs

Sequence in context: A183534 A066040 A318806 * A051237 A064379 A278961

Adjacent sequences: A066016 A066017 A066018 * A066020 A066021 A066022

Keyword

nonn,tabl,nice,more,changed

Author

N. J. A. Sloane, Dec 30 2001

Extensions

Row n=11 and first 3 terms of row n=12 added by Max Alekseyev, Feb 14 2025

Status

approved