A construction for a family of sets and its application to matroids
A construction for a family of sets and its application to matroids
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集合族的构造及其在拟阵中的应用
DOI：
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发表时间：
1981
期刊：
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通讯作者：
J. Dawson
中科院分区：
文献类型：
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作者：
J. Dawson
给定一个有序集合E的子集族A，我们定义一个构造，给出一个与A 1-1对应的集合族B;同样的构造应用于B，则给出A。对于E的每个子集X，（A cap B subseteq X subseteq A cup B）恰好有一对A∈A和相应的B∈B.当族B是E上的拟阵的基集合时，A可以简单地用拟阵的结构来描述。定义一个多项式，在后一种情况下，该多项式是拟阵的Tutte多项式。
Given a family A of subsets of an ordered set E, we define a construction giving a family of sets B in 1–1 correspondence with A; the same construction applied to B then gives A. For each subset X of E, (A cap B subseteq X subseteq A cup B) for exactly one pair of A∈A and corresponding B∈B. When the family B is the basis collection of a matroid on E, A can be described simply in terms of the matroid structure. A polynomial is defined which, in this latter case, is the Tutte polynomial of the matroid.