[seqfan] No. of sign-nonsingular matrices

N. J. A. Sloane njas at research.att.com
Fri Mar 27 01:55:38 CET 2009

Seqfans,  I don't know if this is in the OEIS already.
Could someone work out a few terms?

I saw the definition in the paper "On sign-nonsingular matrices ...",
by Brualdi and Shader, in the Victor Klee Festschrift volume (DIMACS/AMS Series,
Vol 4)

We are looking at n x n matrices A with entries {0,-1,+1}.
We let |A| be the matrix obtained from A by replacing each
entry by its absolute value.

Then the question is, how many such matrices A have the property that

         permanent( |A| ) =  | det A |  ?

(Initially no group acts; later one could count them mod permutations
of rows and columns, possibly allowing transposing.)


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