Justin Loera (University of California, Riverside): Publications - PhilPeople

University of California, Riverside
Department of Philosophy

Undergraduate

5

Counting Integer flows in Networks
with W. Baldoni-Silva and M. Vergne

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 hyperpla…Read more
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.
3

Polyhedral Cones of Magic Cubes and Squares
with M. Ahmed and R. Hemmecke

Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes.