A234943 Array read by antidiagonals: T(i,j) = size of optimal difference triangle set M(i,j).

1, 2, 3, 3, 7, 3, 4, 10, 13, 11, 5, 12, 19, 22, 17, 6, 15, 24, 32, 34, 25, 7, 19, 30, 41, 49, 51, 34, 8, 22, 36, 51, 64, 72, 70, 44, 9, 24, 42, 60, 79, 94, 100, 94, 55, 10, 27, 48, 71

Offset

1,2

Comments

An (n,k) difference triangle set is a set of n blocks of k integers such that the difference sets of the blocks are all disjoint. The "scope" of such a set is defined to be the maximal element, if all blocks are translated such that their least elements are all 0. T(n,k) lists the minimal scope for which an (n,k) difference triangle set exists. - Charlie Neder, Jun 14 2019

References

CRC Handbook of Combinatorial Designs, 1996, p. 315. (But beware errors!)

Links

Table of n, a(n) for n=1..49.

Yeow Meng Chee and Charles J. Colbourn, Constructions for Difference Triangle Sets, arXiv:0712.2553 [cs.IT], 2007.

J. B. Shearer, Difference Triangle Sets: Known optimal solutions.

J. B. Shearer, Difference Triangle Sets: Discoverers.

Example

Array begins:
j\i|   1   2   3  4  5  6  7  8  9  10  11  12  13  14  15
---+-----------------------------------------------------------------
1  |   1   2   3  4  5  6  7  8  9  10  11  12  13  14  15  (A000027)
2  |   3   7  10 12 15 19 22 24 27  31  34  36  39  43  46  (A013574)
3  |   6  13  19 24 30 36 42 48 54  60  66  72  78  84  90  (A013575)
4  |  11  22  32 41 51 60 71 80 91 100 111 120 131 140 151  (A013576)
5  |  17  34  49 64 79  (A013577)
6  |  25  51  72 94
7  |  34  70 100
8  |  44  94
9  |  55 121
10 |  72
11 |  85
12 | 106
13 | 127
14 | 151
15 | 177
  A003022 A010896 A010898
       A010895 A010897 A010899

Crossrefs

Rows and columns give A000027, A013574, A013575, A013576, A013577; A003022, A010895, A010896, A010897, A010898, A010899.

For the number of different optimal triangle difference sets see the corresponding array in A234947.

Sequence in context: A140182 A340753 A239472 * A209494 A082910 A023646

Adjacent sequences: A234940 A234941 A234942 * A234944 A234945 A234946

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Jan 08 2014

Status

approved