On inequivalent factorizations of a cycle

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).

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

References in corpus (1)

• Semiclassical gaps in the density of states of chaotic Andreev billiards

Cited by in corpus (4)

• A Library-Based Synthesis Methodology for Reversible Logic
• Transport moments beyond the leading order
• Semiclassical approach to universality in quantum chaotic transport
• Inequivalent Factorizations of Permutations