cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Dec 30 2001

Keywords

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.

Examples

			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

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.

Links

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.

A036832 Schoenheim bound L_1(n,5,4).

Original entry on oeis.org

1, 5, 9, 18, 26, 50, 66, 113, 149, 219, 273, 397, 476, 659, 787, 1028, 1197, 1549, 1771, 2237, 2550, 3120, 3510, 4273, 4751, 5700, 6324, 7444, 8184, 9595, 10472, 12161, 13254, 15185, 16451, 18800, 20254, 22991, 24743, 27817, 29799, 33433, 35673, 39821, 42454
Offset: 5

Views

Author

N. J. A. Sloane, Jan 11 2002

Keywords

References

  • 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.

Links

Crossrefs

Lower bound to A011983.
A column of A036838.

Programs

  • Maple
    L := proc(v,k,t,l) local i,t1; t1 := l; for i from v-t+1 to v do t1 := ceil(t1*i/(i-(v-k))); od: t1; end; # gives Schoenheim bound L_l(v,k,t). Current sequence is L_1(n,5,4,1).
  • Mathematica
    L[v_, k_, t_, l_] := Module[{i, t1}, t1 = l; For[i = v - t + 1, i <= v, i++, t1 = Ceiling[t1*i/(i - (v - k))]]; t1];
T[n_, k_] := L[n + 2, k + 2, k + 1, 1];
a[n_] := T[n - 2, 3];
Table[a[n], {n, 5, 46}] (* Jean-François Alcover, Mar 07 2023, after Maple code *)

A066009 Covering numbers C(n,7,6).

Original entry on oeis.org

1, 7, 16, 45, 84
Offset: 7

Views

Author

N. J. A. Sloane

Keywords

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.

Links

Crossrefs

Cf. A011983. A column of A066010.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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