3 research outputs found
A bijection between the d-dimensional simplices with distances in {1,2} and the partitions of d+1
We give a construction for the d-dimensional simplices with all distances in
{1,2} from the set of partitions of d+1.Comment: 2 page
Bounds for the minimum diameter of integral point sets
Geometrical objects with integral sides have attracted mathematicians for
ages. For example, the problem to prove or to disprove the existence of a
perfect box, that is, a rectangular parallelepiped with all edges, face
diagonals and space diagonals of integer lengths, remains open. More generally
an integral point set is a set of points in the
-dimensional Euclidean space with pairwise integral distances
where the largest occurring distance is called its diameter. From the
combinatorial point of view there is a natural interest in the determination of
the smallest possible diameter for given parameters and . We
give some new upper bounds for the minimum diameter and some exact
values.Comment: 8 pages, 7 figures; typos correcte