Gilles Schaeffer ; Ekaterina Vassilieva - Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem

dmtcs:3614 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3614
Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem

Authors: Gilles Schaeffer ORCID-iD1; Ekaterina Vassilieva 1

  • 1 Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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.

https://doi.org/10.46298/dmtcs.3614
Source: HAL:hal-01185148v1
Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Harer-Zagier formula,Jackson formula,cactus trees,cacti,permutations,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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