Cycles in Random Sample Permutations
 As an example, the permutation {1, 3, 2, 5, 6, 4, 8, 9, 7, 11, 12, 13, 14, 15, 16, 10} can be written in terms of cycles as (1)(2, 3)(4, 5, 6)(7, 8, 9)(10, 11, 12, 13, 14, 15, 16). For these five cycles black pixels mark the positions {10, 11, 12, 13, 14, 15, 16}. Two colors would mark positions corresponding to members of the two length-three cycles (4, 5, 6) and (7, 8, 9). A fourth color is needed to represent the transposition pair (2, 3) and a fifth color marks the singleton cycle (1). Sorting all pixel color values and partitioning gives the matrix: {{1, 1, 1, 1}, {1, 1, 1, 2}, {2, 2, 3, 3}, {3, 4, 4, 5}}.   "Cycles in Random Sample Permutations" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/CyclesInRandomSamplePermutations/ Contributed by: Michael Schreiber | ||||||||||||||
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