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{\bf Uwe Schauz}
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{\bf Colorings and Orientations of Matrices and Graphs}
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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 partial solution of
the list coloring conjecture and Scheim's equivalency between not
vanishing permanents and the four color theorem. The general
concept of matrix colorings in the background is also connected to
hypergraph colorings and matrix choosability.
\bye