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

页码：1 / 18

页数：18

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