Unimodular triangulations of simplicial cones by short vectors
arXiv:1601.05208
Abstract
We establish a bound for the length of vectors involved in a unimodular triangulation of simplicial cones. The bound is exponential in the square of the logarithm of the multiplicity, and improves previous bounds significantly. The proof is based on a successive reduction of the highest prime divisor of the multiplicity and uses the prime number theorem to control the length of the subdividing vectors.
12 pages, to appear in JCT-A