Type: Article

Total orders realizable as the distances between two sets of points

Maldonado, Gerardo L.; Raggi, Miguel; Roldán-Pensado, Edgardo;

Abstract:

In this note we give a negative answer to a question proposed by Almendra-Hernández and Martínez-Sandoval. Let be positive integers and let and be sets of sizes and in such that every pair of points in defines a unique distance. There is a natural order on induced by the distances between the corresponding points. The question is if all possible orders on can be obtained in this way. We show that the answer is negative when . The case remains open.