On inequivalent factorizations of a cycle Academic Article uri icon


  • We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 ... n) into a product of smaller cycles of given length, on one side, and trees of a certain structure on the other. We use this bijection to count the factorizations with a given number of different commuting factors that can appear in the first and in the last positions, a problem which has found applications in physics. We also provide a necessary and sufficient condition for a set of cycles to be arrangeable into a product evaluating to (1 2 ... n).

author list (cited authors)

  • Berkolaiko, G., Harrison, J. M., & Novaes, M.

complete list of authors

  • Berkolaiko, G||Harrison, JM||Novaes, M

publication date

  • September 2008