Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings
Combinatorics
2023-07-26 v2 Number Theory
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.
Cite
@article{arxiv.2203.03873,
title = {Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings},
author = {Nóra Frankl and Andrey Kupavskii and Arsenii Sagdeev},
journal= {arXiv preprint arXiv:2203.03873},
year = {2023}
}
Comments
10 pages. v2 includes an important historical reference and a few modifications based on the reviews