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Enumeration of Pin-Permutations

Frédérique Bassino 1, Mathilde Bouvel 2, Dominique Rossin 2

(2008-12-19)

In this paper, we study the class of pin-permutations, that is to say of permutations having a pin representation. This class has been recently introduced in an article of Brignall, Huczinska and Vatter, where it is used to find properties (algebraicity of the generating function, decidability of membership) of classes of permutations, depending on the simple permutations this class contains. We give a recursive characterization of the substitution decomposition trees of pin-permutations, which allows us to compute the generating function of this class, and consequently to prove, as it is conjectured, the rationality of this generating function. Moreover, we show that the basis of the pin-permutation class is infinite.

1:	Laboratoire d'informatique de Paris-nord (LIPN)
	CNRS : UMR7030 – Université Paris-Nord - Paris XIII
2:	Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA)
	CNRS : UMR7089 – Université Paris-Diderot - Paris VII

Subject

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Mathematics/Combinatorics

Keyword(s) : Permutation – Generating function – Permutation Pattern

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From: Dominique Rossin <>

Submitted on: Friday, 19 December 2008 17:18:08

Updated on: Saturday, 20 December 2008 08:56:44