{"paper":{"title":"Extremal permutations in routing cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gexin Yu, Junhua He, Louis A. Valentin, Xiaoyan Yin","submitted_at":"2014-04-07T17:11:29Z","abstract_excerpt":"Let $G$ be a graph on $n$ vertices, labeled $v_1,\\ldots,v_n$ and $\\pi$ be a permutation on $[n]:=\\{1,2,\\cdots, n\\}$. Suppose that each pebble $p_i$ is placed at vertex $v_{\\pi(i)}$ and has destination $v_i$. During each step, a disjoint set of edges is selected and the pebbles on each edge are swapped. Let $rt(G, \\pi)$, the routing number for $\\pi$, be the minimum number of steps necessary for the pebbles to reach their destinations.\n  Li, Lu, and Yang prove that $rt(C_n, \\pi)\\le n-1$ for any permutation on $n$-cycle $C_n$ and conjecture that for $n \\geq 5$, if $rt(C_n, \\pi) = n-1$, then $\\pi "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1851","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"}