(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(a_{ij}) = ∑_{p∈Sn} ∏_{i=1}^{n} a_{i,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.