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Matrix discrepancy and the log-rank conjecture

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Given an m × n binary matrix M with | M | = p · m n (where |M| denotes the number of 1 entries), define the discrepancy of M as disc ( M ) = max X ⊂ [ m ] , Y ⊂ [ n ] | | M [ X × Y ] | - p | X | · | Y | | . Using semi... ...