Abstract We introduce techniques for deriving closed form generating functions for enumerating permutations with restricted positions keeping track of various statistics. The method involves evaluating permanents with variables as entries. These are applied to determine the sample size required for a novel sequential importance sampling algorithm for generating random perfect matchings in classes of bipartite graphs.

中文翻译：

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永久生成函数和顺序重要性采样

摘要 我们介绍了推导封闭形式生成函数的技术，用于枚举具有限制位置的排列以跟踪各种统计数据。该方法涉及以变量作为条目评估永久物。这些用于确定新的顺序重要性采样算法所需的样本大小，以在二部图类中生成随机完美匹配。