Counting integer flows in networks
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.
chambers integral flows flow polytopes lattice points rational function manipulation hyperplane arrangements residues transportation problems kostant partition function