Matrix Permanents

Why

The permanent of a matrix $A \in \R ^{n \times m}$ is

\[ \sum_{\sigma \in S_n} \prod_{i = 1}^{n} A_{i, \sigma (i)} \]

where $S_n$ is the symmetric group of degree $n$ (see Permutations).

We denote the permanent of $A$ by $\perm(A)$.

Future editions will include. The reasoning is that several counting problems to do with graphs reduce to permanents of the adjacency matrix. ↩︎