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.
De Loera, J., Vergne, M., Baldoni, M. (2004). Counting integer flows in networks. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 4(3), 277-314 [10.1007/s10208-003-0088-8].
Counting integer flows in networks
BALDONI, MARIA
2004-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
