(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.