Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Josuat-Verges Matthieu

Minimal factorizations of a cycle: a multivariate generating function
Philippe Biane  1  , Matthieu Josuat-Verges  1  
1 : Laboratoire dÍnformatique Gaspard-Monge  (LIGM)  -  Website
Université Paris-Est Marne-la-Vallée, Ecole des Ponts ParisTech, ESIEE [Paris], Fédération de Recherche Bézout, Centre National de la Recherche Scientifique : UMR8049, ESIEE Paris
Université de Paris-Est Marne-la-Vallée, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2 -  France

It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of k cycles of given lengths has a very simple formula: it is nk1 where n is the rank of the underlying symmetric group and k is the number of factors. In particular, this is nn2 for transposition factorizations. The goal of this work is to prove a multivariate generalization of this result. As a byproduct, we get a multivariate analog of Postnikov's hook length formula for trees, and a refined enumeration of final chains of noncrossing partitions. 

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