# Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry

arXiv: https://arxiv.org/abs/1609.05167 · HTML: https://mlsanity.com/paper/1609.05167/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2016.

## Built on by (most cited first, 2 of 2)

- [Double Bubble, Toil and Trouble: Enhancing Certified Robustness through Transitivity](https://mlsanity.com/paper/2210.06077/) (2022)
- [Kissing to Find a Match: Efficient Low-Rank Permutation Representation](https://mlsanity.com/paper/2308.13252/) (2023)

## Abstract (arXiv)

The kissing number of ℝn is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. Mittelmann and Vallentin (2010), based on the semidefinite programming bound of Bachoc and Vallentin (2008), computed the best known upper bounds for the kissing number for several values of n ≤ 23. In this paper, we exploit the symmetry present in the semidefinite programming bound to provide improved upper bounds for n = 9, ldots, 23.