{"paper":{"title":"Noncrossing partitions for periodic braids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eon-Kyung Lee, Sang-Jin Lee","submitted_at":"2016-08-21T00:08:50Z","abstract_excerpt":"An element in Artin's braid group $B_n$ is called periodic if it has a power which lies in the center of $B_n$. The conjugacy problem for periodic braids can be reduced to the following: given a divisor $1\\le d<n-1$ of $n-1$ and an element $\\alpha$ in the super summit set of $\\epsilon^d$, find $\\gamma\\in B_n$ such that $\\gamma^{-1}\\alpha\\gamma=\\epsilon^d$, where $\\epsilon=(\\sigma_{n-1}\\cdots\\sigma_1)\\sigma_1$.\n  In this article we characterize the elements in the super summit set of $\\epsilon^d$ in the dual Garside structure by studying the combinatorics of noncrossing partitions arising from "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05879","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}