Counting Integer flows in Networks

Details Counting Integer flows in Networks Counting Integer flows in Networks

2003-03-19

arxiv.org/abs/math/0303228v1

Mathematics

Combinatorics

Scientific paper

This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics \cite{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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