SETS AVOIDING SIX-TERM ARITHMETIC PROGRESSIONS IN Z6n ARE EXPONENTIALLY SMALL

被引：1

作者：

Pach, Peter Pal ^{[1
,2
]}

Palincza, Richard ^{[1
,2
]}

机构：

[1] Budapest Univ Technol & Econ, Dept Comp Sci & Informat Theory, H-1111 Budapest, Hungary

[2] ELKH, MTA BME Lendulet Arithmet Combinator Res Grp, H-1111 Budapest, Hungary

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2022年 / 36卷 / 02期

关键词：

arithmetic progressions; polynomial method; supersaturation;

D O I：

10.1137/21M1413766

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that sets avoiding six-term arithmetic progressions in Z(6)(n) have size at most 5.709n. It is also pointed out that the "product construction"" does not work in this setting; in particular we show that for the extremal sizes in small dimensions we have r(6) (Z(6)) = 5, r(6) (Z(6)(2)) = 25, and 117 <= r(6) (Z(6)(n)) <= 124.

引用

页码：1135 / 1142

页数：8

共 3 条

[1] SMALL SETS WHICH MEET ALL THE K(N)-TERM ARITHMETIC PROGRESSIONS IN THE INTERVAL [1,N]
BROWN, TC
FREEDMAN, AR
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1989, 51 (02) : 244 - 249
[2] SMALL SETS WHICH MEET ALL THE N-TERM ARITHMETIC PROGRESSIONS IN THE INTERVAL [1,N2]
TRUSS, JK
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1991, 23 : 123 - 127
[3] Progression-free sets in Z4n are exponentially small
Croot, Ernie
Lev, Vsevolod F.
Pach, Peter Pal
ANNALS OF MATHEMATICS, 2017, 185 (01) : 331 - 337

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