Type: Inproceedings

On prescribing total orders for bipartite sets of distances in the Euclidean plane

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

Book Title: XII Latin American Algorithms, Gaphs and Optimization Symposium (LAGOS 2023)

Editor: Cristina Fernandes; Sergio Rajsbaum

Abstract:

In this note we give a negative answer to a question proposed by Almendra-Hernández and Martínez-Sandoval. Let n ? m be positive integers and let X and Y be sets of sizes n and m in Rn-1 such that X U Y is in generic position. There is a natural order on X x Y induced by the distances between the corresponding points. The question is if all possible orders on X x Y can be obtained in this way. We show that the answer is negative when n < m. The case n=m remains open.