# The permanent conjecture

**Conjecture**If is an invertible matrix, then there is an submatrix of so that is nonzero.

If true, this conjecture would imply the nowhere-zero point in a linear mapping conjecture via the Alon-Tarsi polynomial technique. I believe Yang Yu was the first to suggest the following generalization of the permanent conjecture.

**Conjecture (Yu)**If are invertible matrices over the same field, then there is an submatrix of so that is nonzero.

This conjecture when restricted to the field is a consequence of the Alon-Tarsi basis conjecture. In addition to implying the above conjecture, the truth of this conjecture for matrices over the field would imply that every 6-edge-connected graph has a nowhere-zero 3-flow, thus resolving The weak 3-flow conjecture.