We develop a new, powerful method for counting elements in a {\em 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. Finally, we investigate a proposal of Blitvi\'c and Steingr\'imsson as to the range of a parameter for which a particular generating function formed from the occurrence sequences is itself a Stieltjes moment sequence.

翻译：我们发展了一种新的、强大的计数方法，用于计算多重集中的元素。作为首个应用，我们利用该算法研究排列中模式的出现次数。对于长度为3的模式，存在两个Wilf类，其一般行为已有较充分认知。我们对此情形下的部分已知结果进行了适度扩展，并详尽研究了此前鲜有认知的长度为4的模式情形。对于此类模式，存在七个Wilf类，基于大量枚举与精细的级数分析，我们推测了所有类别的渐近行为。最后，我们对Blitvić与Steingrímsson提出的关于某参数取值范围的研究——该参数可使得由出现序列生成的特殊生成函数本身成为Stieltjes矩序列——进行了探讨。