The Enumeration of Maximally Clustered Permutations
نویسندگان
چکیده
The maximally clustered permutations are characterized by avoiding the classical permutation patterns {3421, 4312, 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, 56781234}.
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