Mobius functions of lattices
Mobius functions of lattices
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格子的莫比乌斯函数
DOI：
10.1006/aima.1997.1616
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发表时间：
1997
影响因子：
1.7
通讯作者：
B. Sagan
中科院分区：
文献类型：
--
作者：
A. Blass;B. Sagan
摘要我们介绍了下面设置的晶格中的概念。这可以用来将Rota的断电定理概括为任何有限的晶格。然后，我们展示如何使用该结果来计算和组合在各种示例中解释Mobius函数，包括以优势顺序的非交叉设置分区，洗牌POSET和整数分区。接下来，我们介绍了斯坦利定理的概括，即半模块化晶格因子在整数上的特征多项式。我们还提供了第二个主要定理的某些应用，包括塔玛里晶格。
Abstract We introduce the concept of a bounded below set in a lattice. This can be used to give a generalization of Rota's broken circuit theorem to any finite lattice. We then show how this result can be used to compute and combinatorially explain the Mobius function in various examples including non-crossing set partitions, shuffle posets, and integer partitions in dominance order. Next we present a generalization of Stanley's theorem that the characteristic polynomial of a semimodular supersolvable lattice factors over the integers. We also give some applications of this second main theorem, including the Tamari lattices.