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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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