Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem - Gilles Schaeffer; Ekaterina Vassilieva (Discrete Mathematics & Theoretical Computer Science, 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.