Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings

Frankl, Nora; Kupavskii, Andrey and Sagdeev, Arsenii (2023). Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings. Proceedings of the American Mathematical Society, 151 pp. 2353–2362.

DOI: https://doi.org/10.1090/proc/16254

Abstract

In 2008, Schmidt and Tuller stated a conjecture concerning optimal packing and covering of integers by translates of a given three-point set. In this note, we confirm their conjecture and relate it to several other problems in combinatorics.

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