On inequivalent factorizations of a cycle
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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