最大聚簇置换的enumeration
The enumeration of maximally clustered permutations
摘要：
最大聚类置换的特征在于避免了经典置换模式3421、4312和4321。这个类包含自由编织置换和全交换置换。在这项工作中，我们表明，某些完全可交换的模式类的生成函数可以转换为相应的自由编织和最大聚类模式类的生成函数。而且，这种生成函数的变换是有理的。结果，我们得到了上述模式类的枚举公式以及相应的避免六边形的模式类，其中避免六边形的排列的特征在于避免46718235，46781235，56718234和56781234。
英文摘要：
The maximally clustered permutations are characterized by avoiding the classical permutation patterns 3421, 4312, and 4321. This class contains the freely-braided permutations and the fully-commutative permutations. In this work, we show that the generating functions for certain fully-commutative pattern classes can be transformed to give generating functions for the corresponding freely-braided and maximally clustered pattern classes. Moreover, this transformation of generating functions is rational. As a result, we obtain enumerative formulas for the pattern classes mentioned above as well as the corresponding hexagon-avoiding pattern classes where the hexagon-avoiding permutations are characterized by avoiding 46718235, 46781235, 56718234, and 56781234.
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