Uniqueness of Optimal Point Sets Determining Two Distinct Triangles
Combinatorics
2024-03-27 v1
Abstract
In this paper, we show that the maximum number of points in dimensions determining exactly 2 distinct triangles is . We further show that this maximum is uniquely achieved by the vertices of the -orthoplex. We build upon the work of Hirasaka and Shinohara who determined that the -orthoplex is such an optimal configuration, but did not prove its uniqueness. Further, we present a more elementary argument for its optimality.
Cite
@article{arxiv.1910.00629,
title = {Uniqueness of Optimal Point Sets Determining Two Distinct Triangles},
author = {Hazel N. Brenner and James S. Depret-Guillaume and Eyvindur A. Palsson and Steven Senger},
journal= {arXiv preprint arXiv:1910.00629},
year = {2024}
}
Comments
13 pages, 7 figures