Dittert conjecture

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