Erdős discrepancy problem
In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (1, −1, 1, −1 ...).
Such sequences are commonly studied in discrepancy theory.
Around 1932 mathematician Paul Erdős conjectured that for any infinite ±1-sequence and any integer C, there exist integers k and d such that:
The Erdős Discrepancy Problem asks for a proof or disproof of this conjecture.
In October 2010, this problem was taken up by the Polymath Project.
In September 2015, Terence Tao announced a proof of the conjecture, building on work done in 2010 during Polymath5 (a form of crowdsourcing applied to mathematics) and a suggested link to the Elliott conjecture on pair correlations of multiplicative functions. His proof was published in 2016, as the first paper in the new journal Discrete Analysis.
A Barker code is a sequence of N values of +1 and −1,
such that
for all .
...
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