Abstract
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 language | English (US) |
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Article number | P4.36 |
Journal | Electronic Journal of Combinatorics |
Volume | 28 |
Issue number | 4 |
DOIs | |
State | Published - 2021 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics