TY - JOUR
T1 - On the number of sum-free triplets of sets
AU - Araujo, Igor
AU - Balogh, József
AU - Garcia, Ramon I.
N1 - \u2217Research supported by Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132). \u2020and Moscow Institute of Physics and Technology, Russian Federation. Research supported by NSF RTG Grant DMS-1937241, NSF Grant DMS-1764123, Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132), the Langan Scholar Fund (UIUC), and the Simons Fellowship.
Research supported by Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132). and Moscow Institute of Physics and Technology, Russian Federation. Research supported by NSF RTG Grant DMS-1937241, NSF Grant DMS-1764123, Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132), the Langan Scholar Fund (UIUC), and the Simons Fellowship.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.37236/10170
DO - 10.37236/10170
M3 - Article
AN - SCOPUS:85120411518
SN - 1077-8926
VL - 28
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 4
M1 - P4.36
ER -