关于联系系统横截(Transversal)理论的几个结果

Several Results about Transversal Theory of Linking Systems

本文引进了集对族■=<(x_i,y_i):i∈I>的横截概念。证明了■之所有部分横截的集合形成联系系统。这一结果与 Edmonds 和 Fulkerson 关于拟阵与横截的著名结果类似。本文还给出了■具有某种表示系统的充要条件、Hall定理(集对族情形)以及对称联系系统的 Rado 定理。

The concept of transversals is introduced for family ■=〈(x_i,y_i): i∈I〉 of set pairs.It is proved that the collection of partial transversals of ■ forms a linking system.This result is similar to a well-known theorem of Edmonds and Fulkerson about matroids and transversals. Furthermore a necessary and sufficient condition for ■ to have certain system of representatives,Hall theorem (for families of set pairs),and Rado theorem for symmetric linking systems are also presented in this paper.