Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry

DOI10.1080/10586458.2017.1286273zbMath1401.52028arXiv1609.05167OpenAlexW2963419410WikidataQ111288233 ScholiaQ111288233MaRDI QIDQ4689862

Fabrício Caluza Machado, Fernando Mário de Oliveira Filho

Publication date: 22 October 2018

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.05167

zbMATH Keywords

semidefinite programmingkissing numbersymmetric polynomialsinvariant semidefinite programs

Mathematics Subject Classification ID

Semidefinite programming (90C22) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

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Uses Software

• MPFI

Cites Work

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• New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
• New lower bounds for contact numbers in small dimensions
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• The kissing number in four dimensions
• Motivations for an arbitrary precision interval arithmetic and the MPFI library
• Das Problem der dreizehn Kugeln
• Invariant Semidefinite Programs
• New upper bounds for kissing numbers from semidefinite programming
• High-Accuracy Semidefinite Programming Bounds for Kissing Numbers
• Algorithms in invariant theory