{"paper":{"title":"Arc index of pretzel knots of type $(-p,q,r)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gyo Taek Jin, Hwa Jeong Lee","submitted_at":"2012-04-03T05:06:17Z","abstract_excerpt":"We computed the arc index for some of the pretzel knots $K=P(-p,q,r)$ with $p,q,r\\ge2$, $r\\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\\alpha(K)$ equals the minimal crossing number $c(K)$. If $p\\ge3$ and $q=3$, then $\\alpha(K)=c(K)-1$. If $p\\ge5$ and $q=4$, then $\\alpha(K)=c(K)-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0597","kind":"arxiv","version":3},"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"}