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Cycle Notation for Permutations

means with corresponding -matrix

Note that it is necessary to supply the size of a permutation matrix in $[\sigma, n]$, since fixed points are omitted in cycle notation (i.e., there is a difference between $[(1,2), 2]$ and $[(1,2), 3]$). We prefer cycle notation because one can read off the order and the fixed points of a permutation immediately.