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![](//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Example_permutation_matrix%3B_odd_evening%2C_parted.svg/150px-Example_permutation_matrix%3B_odd_evening%2C_parted.svg.png) ![{\displaystyle {\mathit {6936}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e728c249d9cfd4ba3b84b1528e76e68fb5f176b)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Array_of_permutations%3B_odd_evening%2C_alternating.svg/560px-Array_of_permutations%3B_odd_evening%2C_alternating.svg.png) A211366
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![](//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Example_permutation_matrix%3B_odd_evening%2C_alternating.svg/150px-Example_permutation_matrix%3B_odd_evening%2C_alternating.svg.png) ![{\displaystyle {\mathit {20533}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd79d309707c43f86622639b69ead362e20da99c)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Example_permutation_matrix%3B_transpositions%2C_chains.svg/150px-Example_permutation_matrix%3B_transpositions%2C_chains.svg.png) ![{\displaystyle {\mathit {23616}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f5bafc3855fe29ac35605089cd7bb4057b848183)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Array_of_permutations%3B_transpositions%2C_rows.svg/560px-Array_of_permutations%3B_transpositions%2C_rows.svg.png) A211368 Rows of transpositions
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Example_permutation_matrix%3B_transpositions%2C_rows.svg/150px-Example_permutation_matrix%3B_transpositions%2C_rows.svg.png) ![{\displaystyle {\mathit {5167}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdb2ad0c6914b0b63bb882730463483dccdd1c48)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Array_of_permutations%3B_transpositions.svg/560px-Array_of_permutations%3B_transpositions.svg.png) A211369 Transpositions This array corrsponds to the inverted array of 2-element subsets: In place is the cycle , e.g. in place .
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Example_permutation_matrix%3B_transpositions.svg/150px-Example_permutation_matrix%3B_transpositions.svg.png) ![{\displaystyle {\mathit {36153}}=(18)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d45e02493e0bdbec17b05f8e4621d2a74ea0f76)
In place is the set .
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Array_of_permutations%3B_transpositions%2C_nested.svg/560px-Array_of_permutations%3B_transpositions%2C_nested.svg.png) A100630 Nested transpositions
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![](//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Example_permutation_matrix%3B_transpositions%2C_nested.svg/150px-Example_permutation_matrix%3B_transpositions%2C_nested.svg.png) ![{\displaystyle {\mathit {40319}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/90ff2b52808291760b5220c51307d086f288a58c)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Array_of_permutations%3B_circular_shift%2C_left.svg/560px-Array_of_permutations%3B_circular_shift%2C_left.svg.png) A211370 Circular shifts to the left in an interval
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Example_permutation_matrix%3B_circular_shift%2C_left.svg/150px-Example_permutation_matrix%3B_circular_shift%2C_left.svg.png) ![{\displaystyle {\mathit {5913}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/615adc7776baa2ae8ca3226c0170f4f3f11ae237)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Array_of_permutations%3B_circular_shift%2C_right.svg/560px-Array_of_permutations%3B_circular_shift%2C_right.svg.png) A051683 Circular shifts to the right in an interval
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![](//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Example_permutation_matrix%3B_circular_shift%2C_right.svg/150px-Example_permutation_matrix%3B_circular_shift%2C_right.svg.png) ![{\displaystyle {\mathit {35280}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18d1189856cc55345b19fa7d4f8d89b8e57f9e1d)
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Circular shifts to the left,
i.e. permutations whose cycle notation is of the form :
A007489 = 0, 1, 3, 9, 33, 153, 873, 5913...
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Circular shifts to the right,
i.e. permutations whose cycle notation is of the form :
A001563 = 0, 1, 4, 18, 96, 600, 4320, 35280...
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