We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and the general behaviour of these is reasonably well-known. We slightly extend some of the known results in that case, and exhaustively study the case of patterns of length 4, about which there is little previous knowledge. For such patterns, there are seven Wilf classes, and based on extensive enumerations and careful series analysis, we have conjectured the asymptotic behaviour for all classes.

翻译：我们开发了一种新的、强大的方法来计算多重集合中的元素数量。作为第一个应用，我们使用该算法研究排列中模式出现的次数。对于长度为3的模式，存在两个Wilf类，其一般行为已较为明确。我们对此情形下的部分已知结果进行了轻微扩展，并全面研究了此前知之甚少的长度为4的模式情况。对于长度为4的模式，存在七个Wilf类，基于大量枚举和细致的级数分析，我们推测了所有类别的渐近行为。