Unimodular triangulations of simplicial cones by short vectors

2016/01/20 by von Thaden, Michael, Bruns, Winfried
#11H06 #52B20 #52C07 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/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.

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