论文标题
在加权分区的格子上
On the lattice of weighted partitions
论文作者
论文摘要
我们介绍并研究了通用分区的晶格，称为加权分区。该晶格具有分区晶格的相似特性。通过使用加权分区的图形表示形式，总数由第二种的Stirling数字的连续stirling变换给出。我们在晶格上构建了一个明确的$ el $ $ $ - 标签，这意味着该晶格是$ el $ shellable，因此可壳。我们通过使用最大减少链的图形表示来计算Möbius函数和特征多项式。此外，最大减少链被证明是对标有植根的完整二进制树的培养。
We introduce and study the lattice of generalized partitions, called weighted partitions. This lattice possesses similar properties of the lattice of partitions. By use of the pictorial representation of a weighted partition, the total number is given by the successive Stirling transforms of the Stirling number of the second kind. We construct an explicit $EL$-labeling on the lattice, which implies this lattice is $EL$-shellable and hence shellable. We compute the Möbius function and the characteristic polynomial by use of a pictorial representation of a maximal decreasing chain. Further, a maximal decreasing chain is shown to be bijective to a labeled rooted complete binary tree.
