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Bijective Enumeration of 3-Factorizations of an N-Cycle

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Abstract

This paper is dedicated to the factorizations of the symmetric group. Introducing a new bijection for partitioned 3-cacti, we derive an elegant formula for the number of factorizations of a long cycle into a product of three permutations. As the most salient aspect, our construction provides the first purely combinatorial computation of this number.

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  1. Laboratoire d’Informatique de l’Ecole Polytechnique, 91128, Palaiseau, France

    Ekaterina Vassilieva

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  1. Ekaterina Vassilieva
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Correspondence to Ekaterina Vassilieva.

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Vassilieva, E. Bijective Enumeration of 3-Factorizations of an N-Cycle. Ann. Comb. 16, 367–387 (2012). https://doi.org/10.1007/s00026-012-0138-5

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  • DOI: https://doi.org/10.1007/s00026-012-0138-5

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