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 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.
@article{10_37236_10170,
author = {Igor Araujo and J\'ozsef Balogh and Ramon I. Garcia},
title = {On the number of sum-free triplets of sets},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {4},
doi = {10.37236/10170},
zbl = {1486.05020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10170/}
}
TY - JOUR
AU - Igor Araujo
AU - József Balogh
AU - Ramon I. Garcia
TI - On the number of sum-free triplets of sets
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10170/
DO - 10.37236/10170
ID - 10_37236_10170
ER -
%0 Journal Article
%A Igor Araujo
%A József Balogh
%A Ramon I. Garcia
%T On the number of sum-free triplets of sets
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10170/
%R 10.37236/10170
%F 10_37236_10170
Igor Araujo; József Balogh; Ramon I. Garcia. On the number of sum-free triplets of sets. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10170
