On sets free of sumsets with summands of prescribed size
Javier Cilleruelo, Rafael Tesoro
TL;DR
This paper investigates extremal problems related to sets of integers that avoid sumsets with specific summand sizes, exploring both finite and infinite cases and their links to graph and hypergraph extremal problems.
Contribution
It introduces new extremal problems for sets avoiding certain sumsets and connects these to graph and hypergraph extremal theory.
Findings
Characterization of extremal sets avoiding sumsets of prescribed size
Connections established between sumset problems and hypergraph extremal problems
Results applicable to both finite sets and infinite sequences
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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