On inequivalent factorizations of a cycle

Details On inequivalent factorizations of a cycle On inequivalent factorizations of a cycle

2008-09-20

arxiv.org/abs/0809.3476v2

Mathematics

Combinatorics

19 pages, 9 figures; added a discussion of a correspondence with non-crossing partitions

Scientific paper

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).

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