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
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
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jan 08 2014
STATUS
approved