A note on five dimensional kissing arrangements
| Autor: | Szöllősi, Ferenc |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Workshop on Orthogonal designs and related Combinatorics, Meiji University, Tokyo |
| Databáze: | arXiv |
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