{"paper":{"title":"Remnant inequalities and doubly-twisted conjugacy in free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"P. Christopher Staecker","submitted_at":"2008-06-28T14:20:47Z","abstract_excerpt":"We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms $\\phi$ and $\\psi$ such that certain remnant words from $\\phi$ are longer than the images of generators under $\\psi$.\n  Our first result is a remnant inequality condition which implies that two words $u$ and $v$ are not doubly-twisted conjugate. Further we show that if $\\psi$ is given and $\\phi$, $u$, and $v$ are chosen at random, then the probability that $u$ and $v$ are not doubly-twisted conjugate is 1. In the particular case of singly-twisted conjugacy, this means that if $\\phi$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4687","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"}