Number of A plus B ≠ C solutions in abelian groups and application to counting independent sets in hypergraphs

被引：1

作者：

Semchankau, Aliaksei ^{[1
,2
]}

Shabanov, Dmitry ^{[3
,4
]}

Shkredov, Ilya ^{[2
,5
,6
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Dept Dynam Syst Theory, Leninskie Gory 1, Moscow, Russia

[2] Russian Acad Sci, Steklov Math Inst, Gubkina 8, Moscow, Russia

[3] Moscow Inst Phys & Technol, Lab Combinatorial & Geometr Struct, Inst Skiy 9, Dolgoprudnyi, Moscow Region, Russia

[4] HSE Univ, Fac Comp Sci, Myasnitskaya Str 20, Moscow, Russia

[5] IITP RAS, Bolshoy Karetny 19, Moscow, Russia

[6] Moscow Inst Phys & Technol, Inst Skiy 9, Dolgoprudnyi, Moscow Region, Russia

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2022年 / 100卷

关键词：

ARITHMETIC PROGRESSIONS; GRAPHS;

D O I：

10.1016/j.ejc.2021.103453

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper deals with a problem of Additive Combinatorics. Let G be a finite abelian group of order N. We prove that the number of subset triples A, B, C subset of G such that for any x is an element of A, y is an element of B and z is an element of C one has x+y not equal z equals 3.4(N) + N3(N+1) + O((3 - c(*))(N)) for some absolute constant c(*) > 0. This provides a tight estimate for the number of independent sets in a special 3-uniform linear hypergraph and disproves the conjecture of Cohen et al. (0000). concerning the maximal possible number of independent sets in such hypergraphs on n vertices. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：13

共 20 条

[1] INDEPENDENT SETS IN REGULAR GRAPHS AND SUM-FREE SUBSETS OF FINITE-GROUPS [J].