Non-crossing partitions for classical reflection groups
Non-crossing partitions for classical reflection groups
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DOI：
10.1016/s0012-365x(96)00365-2
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发表时间：
1997-12
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影响因子：
--
通讯作者：
V. Reiner
中科院分区：
文献类型：
--
作者：
V. Reiner
我们为B和D类型的经典反射群引入了非交叉集划分的格的类似物。B类型类似物（首先由Montenegro以不同的形式考虑）证明与原始的非交叉集划分一样表现良好，而D类型类似物几乎同样表现良好。在这两种情况下，它们都是具有对称链分解（B型自对偶）的el -可标记排序格，其秩生成函数、zeta多项式、秩选择链数具有简单的封闭形式。
We introduce analogues of the lattice of non-crossing set partitions for the classical reflection groups of types B and D. The type B analogues (first considered by Montenegro in a different guise) turn out to be as well-behaved as the original non-crossing set partitions, and the type D analogues almost as well-behaved. In both cases, they are EL-labellable ranked lattices with symmetric chain decompositions (self-dual for type B), whose rank-generating functions, zeta polynomials, rank-selected chain numbers have simple closed forms.