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We introduce colorings and orientations of matrices as generalizations of the graph theoretic terms. The permanent per$(A[\zeta|\xi])$ of certain copies $A[\zeta|\xi]$ of a matrix $A$ can be expressed as a weighted sum over the orientations or the colorings of $A$. When applied to incidence matrices of graphs these equations include Alon and Tarsi's theorem about Eulerian orientations and the existence of list colorings. In the case of planar graphs we deduce Ellingham and Goddyn's partialdoi:10.37236/1087 fatcat:egpr77j2a5gubfl2c4o3x7ib74