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Oct 4, 2021 at 12:46 comment added Max Alekseyev Also, if permanent of the 0-1 matrix with elements of $A$ taken by absolute value is zero (which is easy to test), then permanent of $A$ is zero as well.
Oct 4, 2021 at 5:53 history edited YCor CC BY-SA 4.0
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Oct 4, 2021 at 4:50 comment added Anurag Sahay Here's a relevant answer from the cstheory stack exchange. cstheory.stackexchange.com/questions/32885/… Of course, this doesn't answer your question.
Oct 4, 2021 at 4:42 comment added Jacob.Z.Lee That is a good idea. Unfortunately, the permanent of my concerned (1,-1,0)-matrix is always even, I think.
Oct 4, 2021 at 4:17 comment added Max Alekseyev We can sort out some cases by noticing that pemanent and determinant are congruent modulo 2. So, if determinant is odd, then permanent must be nonzero.
Oct 4, 2021 at 4:04 comment added Jacob.Z.Lee yes, it is a (1.-1,0)-matrix.
Oct 4, 2021 at 3:02 comment added LSpice $A(1, -1, 0)$ means all entries are $1$, $-1$, or $0$?
Oct 4, 2021 at 2:42 comment added Jacob.Z.Lee Computing the permanent of a (0,1)-matrix is #P-complete. If given a matrix A(1,-1,0), can we detect it zero or nonzero without computing it out by some methods?
Oct 4, 2021 at 2:34 comment added Will Sawin Isn't this #P-complete?
Oct 4, 2021 at 2:27 history asked Jacob.Z.Lee CC BY-SA 4.0