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Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem

Abstract : 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.
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Gilles Schaeffer, Ekaterina Vassilieva. Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.641-652. ⟨hal-01185148⟩

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