# On the Number of Sum-Free Triplets of Sets

@article{Araujo2021OnTN,
title={On the Number of Sum-Free Triplets of Sets},
author={Igor Araujo and J{\'o}zsef Balogh and Ramon I. Garcia},
journal={Electron. J. Comb.},
year={2021},
volume={28}
}
• Published 15 January 2021
• Mathematics
• Electron. J. Comb.
We count the ordered sum-free triplets of subsets in the group $\mathbb{Z}/p\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \subset \mathbb{Z}/p\mathbb{Z}$ for which the equation $a+b=c$ has no solution with $a\in A$, $b \in B$ and $c \in C$. 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…

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