四行近三重数组的存在谱

中文摘要 AI 辅助

在20世纪50年代和60年代，Agrawal引入了一类实验设计，后来被称为三重数组。Gordeev、Markström和Öhman通过放宽三重数组的所有三个交集性质，提出了近三重数组，允许两个值集中在平均交集大小附近，以及复制数的两个连续值。他们完全解决了三行近三重数组的存在性问题，证明了存在一个$(3\times c,v)$-近三重数组当且仅当$v\geq c\geq 3$，除了$(c,v)\in\{(3,6),(4,6),(5,8)\}$。在本文中，我们进一步研究四行近三重数组的存在性，并证明了存在一个$(4\times c,v)$-近三重数组当且仅当$v\geq c\geq 4$，除了$(c,v)\in\{ (4,9),(5,7),(5,10),(6,8),(7,9),(10,12),(11,13)\}$。

英文摘要

In the 1950s and 1960s, Agrawal introduced a class of experimental designs that later became known as triple arrays. Gordeev, Markström and Öhman proposed near triple arrays by relaxing all three intersection properties of triple arrays, allowing two values concentrated around the average intersection size, as well as two consecutive values for the replication numbers. They completely resolved the existence of near triple arrays with three rows, showing that there exists a $(3\times c,v)$-near triple array if and only if $v\geq c\geq 3$ except for $(c,v)\in\{(3,6),(4,6),(5,8)\}$. In this paper, we further investigate the existence of near triple arrays with four rows and prove that there exists a $(4\times c,v)$-near triple array if and only if $v\geq c\geq 4$ except for $(c,v)\in\{ (4,9),(5,7),(5,10),(6,8),(7,9),(10,12),(11,13)\}$.

发表机构

• Henan Normal University（河南师范大学）
• Yancheng Teachers University（盐城师范学院）

机构由 AI 辅助整理，请以论文原文为准。