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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. Dans cet article, nous construisons une bijection pour 3-cacti partitionnés faisant apparaître une nouvelle formule pour l’énumération des factorisations d’un long cycle en trois permutations ayant un nombre donné de cycles.

Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem