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A234943
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Array read by antidiagonals: T(i,j) = size of optimal difference triangle set M(i,j).
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12
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 315. (But beware errors!)
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LINKS
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EXAMPLE
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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)
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
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CROSSREFS
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For the number of different optimal triangle difference sets see the corresponding array in A234947.
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KEYWORD
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AUTHOR
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STATUS
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approved
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