The density of planar sets avoiding unit distances

DOI10.1007/s10107-023-02012-9zbMATH Open1547.42016MaRDI QIDQ6608036

Dániel Varga, Máté Matolcsi, Adrián Csiszárik, Gergely Ambrus, Unnamed Author

Publication date: 19 September 2024

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

zbMATH Keywords

linear programmingharmonic analysisdistance-avoiding setschromatic number of the plane

Mathematics Subject Classification ID

Linear programming (90C05) Erd?s problems and related topics of discrete geometry (52C10) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Fourier series and coefficients in several variables (42B05)

Cites Work

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• The chromatic number of the plane is at least 5
• On the density of sets of the Euclidean plane avoiding distance 1
• A COUNTEREXAMPLE TO A CONJECTURE OF LARMAN AND ROGERS ON SETS AVOIDING DISTANCE 1
• The realization of distances within sets in Euclidean space
• A treatise on the theory of Bessel functions.

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