On Coverings by Minkowski Balls in the Plane and a Duality

Authors

  • Nikolaj M. Glazunov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Glushkov Institute of Cybernetics, NAS Ukraine

DOI:

https://doi.org/10.7546/CRABS.2024.06.02

Keywords:

lattice covering, Minkowski metric, Minkowski ball, hexagon, covering constant, covering density, thinnest covering

Abstract

Lattice coverings in the real plane by Minkowski balls are studied. We exploit the duality of admissible lattices of Minkowski balls and inscribed convex symmetric hexagons of these balls. An explicit moduli space of the areas of these hexagons is constructed, giving the values of the determinants of corresponding covering lattices. Low and upper bounds for covering constants of Minkowski balls are given. The best known value of covering density of Minkowski ball is obtained. One conjecture and one problem are formulated.

Author Biography

Nikolaj M. Glazunov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Glushkov Institute of Cybernetics, NAS Ukraine

Mailing Addresses:
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8
1113 Sofia, Bulgaria

and

Glushkov Institute of Cybernetics,
NAS Ukraine
Kiev, Ukraine

Email: glanm@yahoo.com

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Published

30-06-2024

How to Cite

[1]
N. Glazunov, “On Coverings by Minkowski Balls in the Plane and a Duality”, C. R. Acad. Bulg. Sci. , vol. 77, no. 6, pp. 801–809, Jun. 2024.

Issue

Section

Mathematics