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Kostant Partitions Functions and Flow Polytopes

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Abstract

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 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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    Welleda Baldoni

  2. Centre de Mathématiques, Ecole Polytechnique, Palaiseau Cedex, F-91128, France

    Michèle Vergne

Authors
  1. Welleda Baldoni
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  2. Michèle Vergne
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Correspondence to Welleda Baldoni.

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Dedicated to Bertram Kostant on the occasion of his 80th birthday

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Baldoni, W., Vergne, M. Kostant Partitions Functions and Flow Polytopes. Transformation Groups 13, 447–469 (2008). https://doi.org/10.1007/s00031-008-9019-8

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