A note on five dimensional kissing arrangements

Ferenc Szöllősi

A note on five dimensional kissing arrangements

Combinatorics 2023-01-23 v1

Authors: Ferenc Szöllősi

Abstract

The kissing number $\tau(d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$ -dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of $40$ unit spheres in dimension $5$ . Our arrangement saturates the best known lower bound on $\tau(5)$ , and refutes a `belief' of Cohn--Jiao--Kumar--Torquato.

Keywords

sphere packings and spherical designs

Cite

@article{arxiv.2301.08272,
  title  = {A note on five dimensional kissing arrangements},
  author = {Ferenc Szöllősi},
  journal= {arXiv preprint arXiv:2301.08272},
  year   = {2023}
}

Comments

Workshop on Orthogonal designs and related Combinatorics, Meiji University, Tokyo

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