On the number of sum-free triplets of sets

Igor Araujo, József Balogh, Ramon I. Garcia

Research output: Contribution to journalArticlepeer-review


We count the ordered sum-free triplets of subsets in the group Z/pZ, i.e., the triplets (A, B, C) of sets A, B, C ⊂ Z/pZ for which the equation a + b = c has no solution with a ∈ A, b ∈ B and c ∈ C. Our main theorem improves on a recent result by Semchankau, Shabanov, and Shkredov using a different and simpler method. Our proof relates previous results on the number of independent sets of regular graphs by Kahn; Perarnau and Perkins; and Csikvári to produce explicit estimates on smaller order terms. We also obtain estimates for the number of sum-free triplets of subsets in a general abelian group.

Original languageEnglish (US)
Article numberP4.36
JournalElectronic Journal of Combinatorics
Issue number4
StatePublished - 2021

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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