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

Author

N. J. A. Sloane, Jan 08 2014

Keywords

• nonn
• tabl
• more

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

Examples

			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
		

References

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

Links

• 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.

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.