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  "body": "\n## Definition\n\nLet $\\sigma \\in S_n$.\nWrite $\\sigma$ as a product of disjoint cycles, and include a $1$-cycle for each fixed point.\nThe cycle type of $\\sigma$ is the multiset of the lengths of these cycles.\n\n## Remarks\n\nThe [[disjoint cycle decomposition|0YWDAZPRPQ]] is unique up to order, so the cycle type is well defined.\nThe lengths add up to $n$, so the cycle type is a partition of $n$.\nFor example, $(1\\ 2)(3\\ 4\\ 5) \\in S_6$ has cycle type $(3, 2, 1)$.\n\n## Explanations\n\n### L1 human\n\nThe cycle type forgets which points are in which cycle and keeps only the sizes of the cycles.\nTwo permutations with the same cycle type have the same shape.\nIn the symmetric group, the shape decides exactly when two permutations are conjugate.\n",
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