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The index $i$ is a fixed point of the parking function $\\pi$ if $\\pi_i=i$. More generally, for $m\\geq 1$, the indices $(i_1, \\dots, i_m)$ where the $i_j$'s are all distinct constitute an $m$-cycle of the parking function $\\pi$ if $\\pi_{i_1}=i_2, \\pi_{i_2}=i_3, \\dots, \\pi_{i_{m-1}}=i_m, \\pi_{i_m}=i_1$. 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