On Sets Free of Sumsets with Summands of Prescribed Size

Abstract

We study extremal problems about sets of integers that do not contain sumsets with summands of prescribed size. We analyse both finite sets and infinite sequences. We also study the connections of these problems with extremal problems of graphs and hypergraphs.

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Correspondence to Rafael Tesoro.

Additional information

Javier Cilleruelo passed away on May 15, 2016.

This work has been supported by MINECO project MTM2014-56350-P and ICMAT Severo Ochoa project SEV-2011-0087.

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Cilleruelo, J., Tesoro, R. On Sets Free of Sumsets with Summands of Prescribed Size. Combinatorica 38, 511–546 (2018). https://doi.org/10.1007/s00493-016-3444-4

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Mathematics Subject Classification (2000)

  • 11B83