计算成分的上升、水平和下降
Counting rises, levels, and drops in compositions
摘要：
$n\in\NN$的组合是一个或多个正整数的有序集合，其和为$n$。被加数的个数称为组成部分的个数。$n$的回文组合是其中被加数以给定顺序或相反顺序相同的$n$的组合。在本文中，我们研究的生成函数的数目组成（分别回文组成）的$n$与$m$部分在一个给定的集合$A\subseteq\NN$的上升，水平和下降的数目。因此，我们得到所有以前已知的结果，这类问题，以及许多新的结果。
英文摘要：
A composition of $n\in\NN$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands is called the number of parts of the composition. A palindromic composition of $n$ is a composition of $n$ in which the summands are the same in the given or in reverse order. In this paper we study the generating function for the number of compositions (respectively palindromic compositions) of $n$ with $m$ parts in a given set $A\subseteq\NN$ with respect to the number of rises, levels, and drops. As a consequence, we derive all the previously known results for this kind of problem, as well as many new results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
