Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem

@inproceedings{Vassilieva2008PartitionedCA,
  title={Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem},
  author={Ekaterina Vassilieva and Gilles Schaeffer},
  year={2008}
}
In this paper we construct a bijection for partitioned 3-cacti that gives raise to a new formula for enumeration of factorizations of the long cycle into three permutations with given number of cycles. Résumé. Dans cet article, nous construisons une bijection pour 3-cacti partitionnés faisant apparaı̂tre une nouvelle formule pour l’énumération des factorisations d’un long cycle en trois permutations ayant un nombre donné de cycles. 

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