By twisting the vertex rational functions in Brion's formula with a matroid M for generalized permutohedra, the authors obtain Q_M(P) whose evaluation at 1 recovers the matroid Euler characteristic while satisfying natural recursive and reciprocity laws.
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A matroidal twist on a formula of Brion
By twisting the vertex rational functions in Brion's formula with a matroid M for generalized permutohedra, the authors obtain Q_M(P) whose evaluation at 1 recovers the matroid Euler characteristic while satisfying natural recursive and reciprocity laws.