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(mathematics, statistical mechanics:) The permanent is a function of square matrices

   a_11 ... a_1n
   a_21 ... a_2n
   ...  ... ...
   a_n1 ... a_nn
defined as the sum over all permutations p of the integers 1...n of the product a_{1,p(1)} * ... * a_{n,p(n)}:
Perm(aij) = p∈Sn i=1n ai,p(i).

Note that it looks a lot like the determinant, except that there the signs of the sum alternate with the permutation. However, while good polynomial algorithms are known for the determinant, no easy way to calculate the permanent is known.