On Packing of Minkowski Balls

Authors

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

DOI:

https://doi.org/10.7546/CRABS.2023.03.01

Keywords:

lattice packing, Minkowski ball, Minkowski metric, critical lattice, optimal lattice packing

Abstract

We investigate lattice packings of Minkowski balls. By the results of the proof of Minkowski conjecture about the critical determinant we divide Minkowski balls into 3 classes: Minkowski balls, Davis balls and  Chebyshev–Cohn balls. We investigate lattice packings of  these balls on  planes with varying Minkowski metric and  search among these packings the optimal packings. In this paper we prove that the optimal lattice packing of the Minkowski, Davis, and Chebyshev–Cohn balls is realized with respect to the sublattices of index two of the critical lattices of corresponding  balls.

Author Biography

Nikolaj M. Glazunov, Glushkov Institute of Cybernetics NASU Kiev and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mailing Address:
Glushkov Institute of Cybernetics NASU,
Kiev

and

Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8

E-mail: glanm@yahoo.com

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Published

27-03-2023

How to Cite

[1]
N. Glazunov, “On Packing of Minkowski Balls”, C. R. Acad. Bulg. Sci. , vol. 76, no. 3, pp. 335–342, Mar. 2023.

Issue

Section

Mathematics