Evaluation of Permanents
Henryk Minc · Proceedings of the Edinburgh Mathematical Society · 1979
The permanent of an m x n matrix A = (aij),m≤n, is defined by where the summation is over all one-to-one functions σ from {1, … ,m} to { 1, …,n}. In other words, the permanent of A is the sum of all thediagonal productsofA, that is, all the products ofmentries ofAno two of which lie in the same row or in the same column. Thus the permanent ofAmay be evaluated by first multiplying all the row sums ofAand then subtracting from the product all terms that contain as factors two or more entries from the same column ofA. This is the idea behind the formulas of Binet and of Ryser.