Abstract:
A permutation class� is a set of permutations that is stable under pattern containment, for example the class of permutations that avoids a given pattern.
The main result of this work is to show that permutation classes
that contain only finitely many simple permutations have growth rates, that is,
the limit \lim c_n^{1/n} exists, wherer c_n being the number of permutations of size n in the class.
The main tool of the proof is a precise analysis of the system of polynomial functional equations that specifies the generating function C(x) = \sum c_n x^n in this case.
This is joint work with Adeline Pierrot.
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