{"paper":{"title":"A topological framework for signed permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Fenix W.D. Huang","submitted_at":"2014-10-17T12:52:52Z","abstract_excerpt":"In this paper we present a topological framework for studying signed permutations and their reversal distance. As a result we can give an alternative approach and interpretation of the Hannenhalli-Pevzner formula for the reversal distance of signed permutations. Our approach utlizes the Poincar\\'e dual, upon which reversals act in a particular way and obsoletes the notion of \"padding\" of the signed permutations. To this end we construct a bijection between signed permutations and an equivalence class of particular fatgraphs, called $\\pi$-maps, and analyze the action of reversals on the latter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4706","kind":"arxiv","version":1},"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"}