Permanent

Summary

The permanent of a square matrix is the sum, over all permutations, of the products of one entry from each row and each column. It is the determinant formula without the signs. For the $0/1$ biadjacency matrix of a bipartite graph, it counts the perfect matchings. Unlike the determinant, it is believed to be hard to compute: computing the permanent of a $0/1$ matrix is #P-complete.