The Dittert conjecture, or Dittert–Hajek conjecture, is a mathematical hypothesis in combinatorics concerning the maximum achieved by a particular function formula_1 of matrices with real, nonnegative entries satisfying a summation condition. The conjecture is due to Eric Dittert and (independently) Bruce Hajek.
Let formula_2 be a square matrix of order formula_3 with nonnegative entries and with formula_4. Its permanent is defined as
formula_5
where the sum extends over all elements formula_6 of the symmetric group. 
The Dittert conjecture asserts that the function formula_7 defined by formula_8 is (uniquely) maximized when formula_9, where formula_10 is defined to be the square matrix of order formula_3 with all entries equal to 1.
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