The Erdös Discrepancy Problem

These data were generated for the Polymath5-project.

Binary sequences of discrepancy 2.

Each of the files below contain one sequence, given as a list of indices for the sequence, such that a position should be +1 or -1 according to the sign of the index. Two files with the same numbers in the file names contain sequences which are equal for the first 25 indices. If the numbers are different then the sequences differ on at least one of the first 25 indices. The sequences have been normalised by setting the first value to 1.

There are no sequences with discrepncy 2 and length more than 2015

Here is a collection of sequences of length 1120 with discrepancy 2.
Here is a collection of plot of the partial sums for random mutliplicative functions, on a log-log scale..

Greedy sequences.

Here are some sequences constructed by the algorithms discussed here.

Solutions to the first semidefinite relaxation.

Here are some solutioyns to the semidefinite programs discussed here.

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