On the characteristic of integral point sets in $\mathbb{E}^m$

Abstract

We generalise the definition of the characteristic of an integral triangle to integral simplices and prove that each simplex in an integral point set has the same characteristic. This theorem is used for an efficient construction algorithm for integral point sets. Using this algorithm we are able to provide new exact values for the minimum diameter of integral point sets.Comment: 9 pages, 1 figur