Active Orders for Matroid Bases
Active Orders for Matroid Bases
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Matroid 基地的活跃订单
DOI：
10.1006/eujc.2001.0491
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Vergnas
中科院分区：
文献类型：
--
作者：
M. Vergnas
我们介绍了三个有序拟阵的基集的排序，定义在基础活动。我们表明，积极的订单有晶格结构。这个性质包含了基的字典序的邻近性，以及乘积序的极大性，这是贪婪算法定理的一种形式。活跃的订单密切相关的Tutte多项式和Orlik？拟阵的所罗门代数。特别是，我们表明，在一个简单的有序拟阵，一个基础是加入其组件的外部格在NBC基础的Orlik？拟阵的所罗门代数。
We introduce three orderings of the basis set of an ordered matroid, defined in terms of basis activities. We show that the active orders have lattice structures. This property contains both the neighboring property of the lexicographic ordering of bases, and the maximality property of the product ordering, a form of the Greedy Algorithm Theorem. The active orders are closely related to the Tutte polynomial and the Orlik?Solomon algebra of a matroid. In particular, we show that, in a simple ordered matroid, a basis is the join in the external lattice of its components in the NBC basis of the Orlik?Solomon algebra of the matroid.