{"paper":{"title":"On inequivalent factorizations of a cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G. Berkolaiko, J.M. Harrison, M. Novaes","submitted_at":"2008-09-20T00:40:45Z","abstract_excerpt":"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)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3476","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"}