I. I. Bogdanov, O. Grigoryan, M. E. Zhukovskii, “On coverings of tori with cubes”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 503,Pages <nobr>30

MATHEMATICS

On coverings of tori with cubes

I. I. Bogdanov^a, O. Grigoryan^b, M. E. Zhukovskii^a

^a Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
^b National Research University Higher School of Economics, Moscow, Russia

Abstract: We obtain new bounds and exact values of the minimum number of cubes with side length $\varepsilon\in(0,1)$ covering the torus $[\mathbb R/\mathbb Z]^3$.

Keywords: covering with cubes, torus, translation.

UDC: 519.147

Presented: V. V. Kozlov
Received: 06.01.2022
Revised: 06.01.2022
Accepted: 09.02.2022

DOI: 10.31857/S2686954322020072