Large-volume open sets in normed spaces without integral distances
arXiv:1401.8174
Abstract
We study open sets in normed spaces attaining a large volume while avoiding pairs of points at integral distance. The proposed task is to find sharp inequalities for the maximum possible -dimensional volume. This problem can be viewed as an opposite to known problems on point sets with pairwise integral or rational distances.
7 pages, 4 figures, presented ar EuroCG 2013