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Kostant partitions functions and flow polytopes. (English) Zbl 1200.52008
Summary: This paper discusses volumes and Ehrhart polynomials in the context of flow polytopes. The general approach that studies these functions via rational functions with poles on an arrangement of hyperplanes and the total residue of such functions allows us, via a unified approach, to reobtain many interesting calculations existing in the literature. In particular we generalize Lidskii formula relating the Ehrhart polynomial to the volume function.

52B12 Special polytopes (linear programming, centrally symmetric, etc.)
05A17 Combinatorial aspects of partitions of integers
11D45 Counting solutions of Diophantine equations
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
Full Text: DOI
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