# permanent

## Primary tabs

Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

15A15 Determinants, permanents, other special matrix functions

### Perm(A)*Perm(B)=Perm(AB) ?

Is it true that for any two matrices A,B:
Perm(A)*Perm(B)=Perm(AB)
where Perm(A) is the permanent of A.
(The equation is true for Determinants)

### Re: Perm(A)*Perm(B)=Perm(AB) ?

If I'm not mistaken:

1 0 * 1 1 = 1 1
1 1 0 1 1 2

Permanents: 1 * 1 != 3

Regards

T.

(I'm not 100% sure about the complexity of Gauss algorithm for rationals, but my guess is that such a formula would give you a (way too) good way to compute the permanent, a problem that is #P-hard (cp. Jerrum et al., A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries, JACM 51 (2004) and some survey article of Jerrum on the subject).