An element in Artin's braid group BnBn is called periodic if it has a power that lies in the center of BnBn. The conjugacy problem for periodic braids can be reduced to the following: given a divisor 1⩽d<n−11⩽d<n−1 of n−1n−1 and an element α   in the super summit set of eded, find γ∈Bnγ∈Bn such that γ−1αγ=edγ−1αγ=ed, where e=(σn−1⋯σ1)σ1e=(σn−1⋯σ1)σ1.#R##N##R##N#In this article we characterize the elements in the super summit set of eded in the dual Garside structure by studying the combinatorics of noncrossing partitions arising from periodic braids. Our characterization directly provides a conjugating element γ  . And it determines the size of the super summit set of eded by using the zeta polynomial of the noncrossing partition lattice.
['Eon-Kyung Lee', 'Sang-Jin Lee']
Noncrossing partitions for periodic braids