Unimodular triangulations of simplicial cones by short vectors

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. (C) 2017 Elsevier Inc. All rights reserved.