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