permanent of (-1,1) matrices

[Gordon Royle]

I concur with your calculations...

HOWEVER.. if we look on MathSciNet at the review of the Krauter/Seifter
paper, the conjecture is stated slightly, but significantly, differently..

Let A(n,m) denote the nxn \pm 1 matrix with m -1's on the diagonal

Conjecture 1: For n >= 5, the absolute value of the permanent of an nxn \pm
1 matrix A (not equal to A(n,n-1)) is strictly less than the permanent of
A(n,n-1).

Conjecture 2: For n >= 6, the absolute value of the permanent of an nxn \pm
1 matrix A (other than A(n,n) and A(n,n-1)) is strictly less than the
permanent of A(n,n).


In other words.. for n at least 6, A(n,n-1) is best and A(n,n) is second
best...