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# Inside-Out Polytopes

@inproceedings{Beck2006InsideOutP, title={Inside-Out Polytopes}, author={Matthias Beck and San Francisco State University Thomas Zaslavsky}, year={2006} }

- Published 2006

We present a common generalization of counting lattice points in rational poly-topes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart's theory of lattice-point counting to a convex polytope dissected by a hyperplane arrangement. We particularly develop the applications to graph and… CONTINUE READING