部分序和与$P$ -分拆
Partially Ordinal Sums and $P$-partitions
摘要：
给出了偏序集$P$的$P$ -划分的生成函数$f_P(\x)$的一种计算方法。其思想是在偏序集上引入两种变换，并通过递归地应用这些变换来计算$f_P(\x)$。作为应用，我们考虑了偏序集的$n$拷贝的部分序和$P_n$，它推广了直和序数和.我们证明了序列$\{f_{P_n}(\x)\}_{n\ge 1}$满足关于$n$的递归关系的有限系统。我们通过几个例子来说明这个方法，包括一类三棱偏序集和多立方偏序集。
英文摘要：
We present a method of computing the generating function $f_P(\x)$ of $P$-partitions of a poset $P$. The idea is to introduce two kinds of transformations on posets and compute $f_P(\x)$ by recursively applying these transformations. As an application, we consider the partially ordinal sum $P_n$ of $n$ copies of a given poset, which generalizes both the direct sum and the ordinal sum. We show that the sequence $\{f_{P_n}(\x)\}_{n\ge 1}$ satisfies a finite system of recurrence relations with respect to $n$. We illustrate the method by several examples, including a kind of 3-rowed posets and the multi-cube posets.
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