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Foundations of Computational Mathematics

, Volume 4, Issue 3, pp 277–314 | Cite as

Counting Integer Flows in Networks

  • W. Baldoni-Silva
  • J. A. De Loera
  • M. Vergne
Article

Abstract

This paper discusses analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory, representation theory, and statistics. Our methods are based on the study of rational functions with poles on arrangements of hyperplanes; they surpass traditional exhaustive enumeration and can even yield formulas when the input data contains some parameters. We also discuss the calculation of chambers in detail because it is a necessary subroutine.

Integral flows Flow polytopes Lattice points Rational function manipulation Hyperplane arrangements Residues Transportation problems Kostant partition function Chambers 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 00133 RomaItaly
  2. 2.Department of Mathematics, University of California, Davis, CA 95616USA
  3. 3.Centre de Mathématiques, Ecole Polytechnique, F-91128, Palaiseau CedexFrance

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