關於集合系對的研究

Abstract

一個 (0,1) -矩陣的行向量及列向量可以分別被看成一個集合系對(set system) 的特徵向量。在這篇論文中，我們透過這個模型探討一組集合系對的disjunct性質及其從相交個數的觀點探討一些其他的組合性質。同時，本文也包含了我們針對Hirasaka所提出利用群的乘積建構一個disjunct矩陣的方法，所做的一些修正。

The row vectors and the column vectors of a (0,1)-matrix can be treated as characteristic vectors of a pair of set systems respectively. With this model, we study in this thesis pairs of set systems with disjunctness up to some degrees and with some other combinatorial properties in terms of the intersection sizes among them. Some modifications of Hirasaka’s construction of disjunct matrices in terms of products of groups are included.