论文标题
广义有序设置分区
Generalized Ordered Set Partitions
论文作者
论文摘要
在本文中，我们考虑通过对列表大小施加条件获得的有序固定分区，因此第一个$ r $元素分别处于不同的块中。我们引入了LAH数字的概括。对于这个新的组合序列，我们得出其指数生成函数，某些复发关系和组合身份。我们使用组合参数，生成函数，符号方法和Riordan数组来证明并呈现结果。对于某些具体情况，我们通过两个POSET家族为广义LAH数字的反基质提供了组合解释。
In this paper, we consider ordered set partitions obtained by imposing conditions on the size of the lists, and such that the first $r$ elements are in distinct blocks, respectively. We introduce a generalization of the Lah numbers. For this new combinatorial sequence we derive its exponential generating function, some recurrence relations, and combinatorial identities. We prove and present results using combinatorial arguments, generating functions, the symbolic method and Riordan arrays. For some specific cases we provide a combinatorial interpretation for the inverse matrix of the generalized Lah numbers by means of two families of posets.
