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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 ","authors_text":"Gexin Yu, Junhua He, Louis A. 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