The enumeration of maximally clustered permutations

Details The enumeration of maximally clustered permutations The enumeration of maximally clustered permutations

2007-04-26

arxiv.org/abs/0704.3469v2

Mathematics

Combinatorics

17 pages; corrected typos, added new section

Scientific paper

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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