New Lower Bounds for Cap Sets

被引：4
|
作者：
Tyrrell, Fred [1 ]
机构：
[1] Univ Bristol, Fry Bldg, Bristol, England
来源：
DISCRETE ANALYSIS | 2023年
关键词：
cap sets; finite field; arithmetic progressions; SAT solver; SUBSETS;
D O I：
10.19086/da.91076
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A cap set is a subset of F-3(n) with no solutions to x + y + z = 0 other than when x = y = z. In this paper, we provide a new lower bound on the size of a maximal cap set. Building on a construction of Edel, we use improved computational methods and new theoretical ideas to show that, for large enough n, there is always a cap set in F-3(n) of size at least 2.218(n).
引用
收藏
页码：1 / 18
页数：18
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