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

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- by Nóra Frankl, Andrey Kupavskii and Arsenii Sagdeev
- Proc. Amer. Math. Soc.
**151**(2023), 2353-2362 - DOI: https://doi.org/10.1090/proc/16254
- Published electronically: March 14, 2023
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## 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.## References

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## Bibliographic Information

**Nóra Frankl**- Affiliation: School of Mathematics and Statistics, The Open University, Milton Keynes, United Kingdom; and Alfréd Rényi Institute of Mathematics, Budapest, Hungary
- Email: nfrankl@ou.ac.uk
**Andrey Kupavskii**- Affiliation: MIPT, Moscow, Russia; and G-SCOP, Université Grenoble-Alpes, CNRS, France
- MR Author ID: 881077
- Email: kupavskii@ya.ru
**Arsenii Sagdeev**- Affiliation: MIPT, Moscow, Russia; and Alfréd Rényi Institute of Mathematics, Budapest, Hungary
- MR Author ID: 1211056
- ORCID: 0000-0001-8699-2204
- Email: sagdeevarsenii@gmail.com
- Received by editor(s): March 11, 2022
- Received by editor(s) in revised form: July 28, 2022
- Published electronically: March 14, 2023
- Additional Notes: The research was supported by the RSF grant N 21-71-10092

Supported in part by ERC Advanced Grant ‘GeoScape’. - Communicated by: Isabella Novik
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**151**(2023), 2353-2362 - MSC (2020): Primary 05B40
- DOI: https://doi.org/10.1090/proc/16254
- MathSciNet review: 4576303