New lower bounds for van der Waerden numbers

被引：0
|
作者：
Green, Ben [1 ]
机构：
[1] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6RE, England
来源：
FORUM OF MATHEMATICS PI | 2022年 / 10卷
关键词：
D O I：
10.1017/fmp.2022.12
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that there is a red-blue colouring of [N] with no blue 3-term arithmetic progression and no red arithmetic progression of length e(C(log N)3/4(log log )(N))(1/)(4). Consequently, the two-colour van der Waerden number w(3, k) is bounded below by k(b(k)), where b(k) = c(log k/1og log k)(1/3). Previously it had been speculated, supported by data, that w(3, k) = O(k(2)).
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页数：51
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