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math.MG2024
On lower bounds of the density of planar periodic sets without unit distances
Alexander Tolmachev
Determining the maximal density of planar sets without unit distances is a fundamental problem in combinatorial geometry. This paper investigates lower bounds f…
math.MG2024
Optimal partitions of the flat torus into parts of smaller diameter
Dmitry Protasov, Alexander Tolmachev, Vsevolod Voronov
We consider the problem of partitioning a two-dimensional flat torus into sets in order to minimize the maximal diameter of a part. For we give numerical…