Longest constrained sequences: Difference between revisions
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The numbers in square brackets show (what we know of) the length of the longest sequence satisfying the given constraints exactly. The notation <math>a=b</math> is shorthand for <math>T_a(x) = T_b(x)</math>, and <math>a=-b</math> for <math>T_a(x) = -T_b(x)</math>. | The numbers in square brackets show (what we know of) the length of the longest sequence of discrepancy 2 satisfying the given constraints exactly. The notation <math>a=b</math> is shorthand for <math>T_a(x) = T_b(x)</math>, and <math>a=-b</math> for <math>T_a(x) = -T_b(x)</math>. | ||
1 = +2 : [170] | 1 = +2 : [170] | ||
1 = -2 : [>=974] | 1 = -2 : [>=974] | ||
1 = -2, 1 = +3 : [188] | |||
1 = -2, 1 = -3 : [470] | 1 = -2, 1 = -3 : [470] | ||
1 = -2, 1 = +5 : [356] | 1 = -2, 1 = +5 : [356] | ||
1 = -2, 1 = -5 : [>=974] | 1 = -2, 1 = -5 : [>=974] | ||
1 = -2, 1 = -5, 11 = -13 [>=974] | 1 = -2, 1 = -5, 1 = +7 : [>=566] | ||
2 = -3 : [>= | 1 = -2, 1 = -5, 1 = -7 : [284] | ||
1 = -2, 1 = -5, 11 = -13 : [>=974] | |||
1 = -2, 1 = -5, 11 = -13, 17 = -19 : [974] | |||
1 = -2, 1 = -5, 11 = -13, 17 = -19, 23 = +29 : [974] | |||
1 = -2, 1 = -5, 11 = -13, 17 = -19, 23 = +29, 23 = -31 : [854] | |||
1 = +3 : [188] | |||
1 = -3 : [>=575] | |||
1 = -3, 1 = -5 : [>=476] | |||
1 = -3, 1 = +5 : [>=376] | |||
1 = -3, 2 = +5 : [>=506] | |||
1 = -3, 2 = +5, 1 = -11 : [506] | |||
1 = +32 : [>=417] | |||
2 = +3 : [>=549*] | |||
2 = -3 : [>=641] | |||
* Asterisk means that a depth-first search with a little look-ahead showed that the maximum is finite, but the actual maximum may be slightly above that shown. | |||
Latest revision as of 10:21, 8 October 2010
The numbers in square brackets show (what we know of) the length of the longest sequence of discrepancy 2 satisfying the given constraints exactly. The notation [math]\displaystyle{ a=b }[/math] is shorthand for [math]\displaystyle{ T_a(x) = T_b(x) }[/math], and [math]\displaystyle{ a=-b }[/math] for [math]\displaystyle{ T_a(x) = -T_b(x) }[/math].
1 = +2 : [170] 1 = -2 : [>=974] 1 = -2, 1 = +3 : [188] 1 = -2, 1 = -3 : [470] 1 = -2, 1 = +5 : [356] 1 = -2, 1 = -5 : [>=974] 1 = -2, 1 = -5, 1 = +7 : [>=566] 1 = -2, 1 = -5, 1 = -7 : [284] 1 = -2, 1 = -5, 11 = -13 : [>=974] 1 = -2, 1 = -5, 11 = -13, 17 = -19 : [974] 1 = -2, 1 = -5, 11 = -13, 17 = -19, 23 = +29 : [974] 1 = -2, 1 = -5, 11 = -13, 17 = -19, 23 = +29, 23 = -31 : [854] 1 = +3 : [188] 1 = -3 : [>=575] 1 = -3, 1 = -5 : [>=476] 1 = -3, 1 = +5 : [>=376] 1 = -3, 2 = +5 : [>=506] 1 = -3, 2 = +5, 1 = -11 : [506] 1 = +32 : [>=417] 2 = +3 : [>=549*] 2 = -3 : [>=641]
- Asterisk means that a depth-first search with a little look-ahead showed that the maximum is finite, but the actual maximum may be slightly above that shown.
