Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings-Reference-Cited by-同舟云学术

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

Published:2023-03-14 Issue: Volume: Page:
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Frankl Nóra,Kupavskii Andrey,Sagdeev Arsenii

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.

Funder

European Research Council

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/0000-000-00/S0002-9939-2023-16254-1/proc16254_AM.pdf

Reference19 articles.

1. Polychromatic colorings on the integers;Axenovich, Maria;Integers,2019

2. Periodicity and decidability of tilings of ℤ²;Bhattacharya, Siddhartha;Amer. J. Math.,2020

3. On covering by translates of a set;Bollobás, Béla;Random Structures Algorithms,2011

4. Tiling the integers with translates of one finite set;Coven, Ethan M.;J. Algebra,1999

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Tilings of Z with multisets of distances;Discrete Mathematics;2024-09

2. Max-norm Ramsey theory;European Journal of Combinatorics;2024-05

3. Two-Colorings of Normed Spaces with No Long Monochromatic Unit Arithmetic Progressions;Doklady Mathematics;2022-11

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