The Dittert conjecture, or DittertâÂÂHajek 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 (independently) 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 (uniquely) maximized when , where is defined to be the square matrix of order with all entries equal to 1.