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On the maximum number of integer colourings with forbidden monochromatic sums
Mathematics Institute, University of Warwick, Coventry, United Kingdom.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Mathematical Institute, University of Oxford, Oxford, United Kingdom.
2021 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 28, no 1, article id P1.59Article in journal (Refereed) Published
Abstract [en]

Let f(n, r) denote the maximum number of colourings of A ⊆ {1, …, n} with r colours such that each colour class is sum-free. Here, a sum is a subset {x, y, z} such that x + y = z. We show that f(n, 2) = 2⌈n/2⌉, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of f(n, r) for r ≤ 5. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.

Place, publisher, year, edition, pages
2021. Vol. 28, no 1, article id P1.59
National Category
Discrete Mathematics Other Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-182051DOI: 10.37236/8824ISI: 000652332700001Scopus ID: 2-s2.0-85103005821OAI: oai:DiVA.org:umu-182051DiVA, id: diva2:1544956
Available from: 2021-04-16 Created: 2021-04-16 Last updated: 2023-09-05Bibliographically approved

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Sharifzadeh, Maryam

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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Output format
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