Enumeration of pin-permutations
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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 by Brignall, Huczynska and Vatter who used it 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 by Brignall, Ruškuc and Vatter, the rationality of this generating function. Moreover, we show that the basis of the pin-permutation class is infinite.
@article{10_37236_544,
author = {Fr\'ed\'erique Bassino and Mathilde Bouvel and Dominique Rossin},
title = {Enumeration of pin-permutations},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/544},
zbl = {1217.05021},
url = {http://geodesic.mathdoc.fr/articles/10.37236/544/}
}
Frédérique Bassino; Mathilde Bouvel; Dominique Rossin. Enumeration of pin-permutations. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/544
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