Title:Simple counting of integer points via irrationality.
Session Name:
Special Session on Extremal and Probabilistic Combinatorics
Author: Frank Sottile
Abstract:
In 1988 Brion gave a formula for the integer points in
a rational polytope in Rd in terms of certain rational
generating functions associated to its vertices. His proof
used the equivariant K-theory of singular toric varieties,
and his formula led to Barvinok's polynomial-time algorithm
for the integer points in a polytope.
I will present a proof of Brion's Theorem based on simple
counting, using the technique of irrational decompositions.
This is joint work with Beck and Haase. I will also describe
how Koeppe uses irrational decompositions to dramatically
improve the performance of Barvinok's algorithm.