On inequivalent factorizations of a cycle
Combinatorics
2010-12-14 v2
Abstract
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).
Cite
@article{arxiv.0809.3476,
title = {On inequivalent factorizations of a cycle},
author = {G. Berkolaiko and J. M. Harrison and M. Novaes},
journal= {arXiv preprint arXiv:0809.3476},
year = {2010}
}
Comments
19 pages, 9 figures; added a discussion of a correspondence with non-crossing partitions