Abstract In 1930s Paul Erdős conjectured that for any positive integer C in any infinite ±1 sequence (xn) there exists a subsequence x d , x 2d , x 3d , . . . , x kd , for some positive integers k and d, such that | k i=1 x id |> C. The conjecture has been referred to as one of the major open problems in combinatorial number theory and discrepancy theory. For the particular case of C = 1 a human proof of the conjecture exists; for C = 2 a bespoke computer program had generated sequences of length 1124 of discrepancy 2, but the status of the conjecture remained open even for such a small bound. We show that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solver, one can obtain a discrepancy 2 sequence of length 1160 and a proof of the Erdős discrepancy conjecture for C = 2, claiming that no discrepancy 2 sequence of length 1161, or more, exists. We also present our partial results for the case of C = 3.
The proof of Erdös' discrepancy conjecture for C = 2 from 2014 REF has been touted as one of the largest mathematical proofs and produced approx.
A SAT Attack on the Erdos Discrepancy Conjecture
ArXiv
ArXiv
Computer Science Mathematics