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In mathematics, a ±1–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. ==Erdős discrepancy problem== 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.〔(【引用サイトリンク】 The Erdős discrepancy problem )〕 In February 2014, Alexei Lisitsa and Boris Konev of the University of Liverpool, UK, showed that every sequence of 1161 or more elements satisfies the conjecture in the special case ''C'' = 2, which proves the conjecture for ''C'' ≤ 2. This was the best such bound available at the time. Their proof relies on a SAT-solver computer algorithm whose output takes up 13 gigabytes of data, more than the entire text of Wikipedia, so it cannot be verified by human mathematicians. However, human checking may not be necessary: if an independent computer verification returns the same results, the proof is likely to be correct. 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)〔( article ), New Statesman 30 Sep 15 retrieved 21.10.2015〕 and a suggested link to the Elliott conjecture on pair correlations of multiplicative functions.〔(article ), New Statesman 25 Sep 15 retrieved 21.10.2015〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「±1-sequence」の詳細全文を読む スポンサード リンク
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