Counting Integer flows in Networks
W. Baldoni-Silva, J. A. De Loera, M. Vergne
Abstract
This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory Jaeger, representation theory kirillov, and statistics persi. Our methods clearly surpass traditional exhaustive enumeration and other algorithms and can even yield formulas when the input data contains some parameters. These methods are based on the study of rational functions with poles on arrangements of hyperplanes.
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