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Bit permutations by cycle type
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- Compare: Permutations by cycle type
The following table shows the bit permutations corresponding to the 5!=120 permutations of 5 elements ordered by cycle type.
| There are | 1 | , | 10 | , | 20 | , | 15 | , | 30 | , | 20 | , | 24 (row 5 of  A181897) permutations of 5 elements
|
| with cycle type | 0 | , | 1 (2) | , | 2 (3) | , | 3 (2+2) | , | 4 (4) | , | 5 (3+2) | , | 6 (5). |
The violet numbers represent partitions by index numbers of A194602 (compare this table).
The cycle type of the n-th finite permutation is shown in A198380.
The bit permutations in natural order can be found here.
0 --> 0 1 2 3 4 --> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 --> 1 0 2 3 4 --> 0 2 1 3 4 6 5 7 8 10 9 11 12 14 13 15 16 18 17 19 20 22 21 23 24 26 25 27 28 30 29 31 2 --> 0 2 1 3 4 --> 0 1 4 5 2 3 6 7 8 9 12 13 10 11 14 15 16 17 20 21 18 19 22 23 24 25 28 29 26 27 30 31 5 --> 2 1 0 3 4 --> 0 4 2 6 1 5 3 7 8 12 10 14 9 13 11 15 16 20 18 22 17 21 19 23 24 28 26 30 25 29 27 31 6 --> 0 1 3 2 4 --> 0 1 2 3 8 9 10 11 4 5 6 7 12 13 14 15 16 17 18 19 24 25 26 27 20 21 22 23 28 29 30 31 14 --> 0 3 2 1 4 --> 0 1 8 9 4 5 12 13 2 3 10 11 6 7 14 15 16 17 24 25 20 21 28 29 18 19 26 27 22 23 30 31 21 --> 3 1 2 0 4 --> 0 8 2 10 4 12 6 14 1 9 3 11 5 13 7 15 16 24 18 26 20 28 22 30 17 25 19 27 21 29 23 31 24 --> 0 1 2 4 3 --> 0 1 2 3 4 5 6 7 16 17 18 19 20 21 22 23 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31 54 --> 0 1 4 3 2 --> 0 1 2 3 16 17 18 19 8 9 10 11 24 25 26 27 4 5 6 7 20 21 22 23 12 13 14 15 28 29 30 31 80 --> 0 4 2 3 1 --> 0 1 16 17 4 5 20 21 8 9 24 25 12 13 28 29 2 3 18 19 6 7 22 23 10 11 26 27 14 15 30 31 105 --> 4 1 2 3 0 --> 0 16 2 18 4 20 6 22 8 24 10 26 12 28 14 30 1 17 3 19 5 21 7 23 9 25 11 27 13 29 15 31
3 --> 2 0 1 3 4 --> 0 2 4 6 1 3 5 7 8 10 12 14 9 11 13 15 16 18 20 22 17 19 21 23 24 26 28 30 25 27 29 31 4 --> 1 2 0 3 4 --> 0 4 1 5 2 6 3 7 8 12 9 13 10 14 11 15 16 20 17 21 18 22 19 23 24 28 25 29 26 30 27 31 8 --> 0 3 1 2 4 --> 0 1 4 5 8 9 12 13 2 3 6 7 10 11 14 15 16 17 20 21 24 25 28 29 18 19 22 23 26 27 30 31 11 --> 3 1 0 2 4 --> 0 4 2 6 8 12 10 14 1 5 3 7 9 13 11 15 16 20 18 22 24 28 26 30 17 21 19 23 25 29 27 31 12 --> 0 2 3 1 4 --> 0 1 8 9 2 3 10 11 4 5 12 13 6 7 14 15 16 17 24 25 18 19 26 27 20 21 28 29 22 23 30 31 15 --> 3 0 2 1 4 --> 0 2 8 10 4 6 12 14 1 3 9 11 5 7 13 15 16 18 24 26 20 22 28 30 17 19 25 27 21 23 29 31 19 --> 2 1 3 0 4 --> 0 8 2 10 1 9 3 11 4 12 6 14 5 13 7 15 16 24 18 26 17 25 19 27 20 28 22 30 21 29 23 31 20 --> 1 3 2 0 4 --> 0 8 1 9 4 12 5 13 2 10 3 11 6 14 7 15 16 24 17 25 20 28 21 29 18 26 19 27 22 30 23 31 30 --> 0 1 4 2 3 --> 0 1 2 3 8 9 10 11 16 17 18 19 24 25 26 27 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 31 38 --> 0 4 2 1 3 --> 0 1 8 9 4 5 12 13 16 17 24 25 20 21 28 29 2 3 10 11 6 7 14 15 18 19 26 27 22 23 30 31 45 --> 4 1 2 0 3 --> 0 8 2 10 4 12 6 14 16 24 18 26 20 28 22 30 1 9 3 11 5 13 7 15 17 25 19 27 21 29 23 31 48 --> 0 1 3 4 2 --> 0 1 2 3 16 17 18 19 4 5 6 7 20 21 22 23 8 9 10 11 24 25 26 27 12 13 14 15 28 29 30 31 56 --> 0 4 1 3 2 --> 0 1 4 5 16 17 20 21 8 9 12 13 24 25 28 29 2 3 6 7 18 19 22 23 10 11 14 15 26 27 30 31 59 --> 4 1 0 3 2 --> 0 4 2 6 16 20 18 22 8 12 10 14 24 28 26 30 1 5 3 7 17 21 19 23 9 13 11 15 25 29 27 31 74 --> 0 3 2 4 1 --> 0 1 16 17 4 5 20 21 2 3 18 19 6 7 22 23 8 9 24 25 12 13 28 29 10 11 26 27 14 15 30 31 78 --> 0 2 4 3 1 --> 0 1 16 17 2 3 18 19 8 9 24 25 10 11 26 27 4 5 20 21 6 7 22 23 12 13 28 29 14 15 30 31 81 --> 4 0 2 3 1 --> 0 2 16 18 4 6 20 22 8 10 24 26 12 14 28 30 1 3 17 19 5 7 21 23 9 11 25 27 13 15 29 31 99 --> 3 1 2 4 0 --> 0 16 2 18 4 20 6 22 1 17 3 19 5 21 7 23 8 24 10 26 12 28 14 30 9 25 11 27 13 29 15 31 103 --> 2 1 4 3 0 --> 0 16 2 18 1 17 3 19 8 24 10 26 9 25 11 27 4 20 6 22 5 21 7 23 12 28 14 30 13 29 15 31 104 --> 1 4 2 3 0 --> 0 16 1 17 4 20 5 21 8 24 9 25 12 28 13 29 2 18 3 19 6 22 7 23 10 26 11 27 14 30 15 31
7 --> 1 0 3 2 4 --> 0 2 1 3 8 10 9 11 4 6 5 7 12 14 13 15 16 18 17 19 24 26 25 27 20 22 21 23 28 30 29 31 16 --> 2 3 0 1 4 --> 0 4 8 12 1 5 9 13 2 6 10 14 3 7 11 15 16 20 24 28 17 21 25 29 18 22 26 30 19 23 27 31 23 --> 3 2 1 0 4 --> 0 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15 16 24 20 28 18 26 22 30 17 25 21 29 19 27 23 31 25 --> 1 0 2 4 3 --> 0 2 1 3 4 6 5 7 16 18 17 19 20 22 21 23 8 10 9 11 12 14 13 15 24 26 25 27 28 30 29 31 26 --> 0 2 1 4 3 --> 0 1 4 5 2 3 6 7 16 17 20 21 18 19 22 23 8 9 12 13 10 11 14 15 24 25 28 29 26 27 30 31 29 --> 2 1 0 4 3 --> 0 4 2 6 1 5 3 7 16 20 18 22 17 21 19 23 8 12 10 14 9 13 11 15 24 28 26 30 25 29 27 31 55 --> 1 0 4 3 2 --> 0 2 1 3 16 18 17 19 8 10 9 11 24 26 25 27 4 6 5 7 20 22 21 23 12 14 13 15 28 30 29 31 60 --> 0 3 4 1 2 --> 0 1 8 9 16 17 24 25 2 3 10 11 18 19 26 27 4 5 12 13 20 21 28 29 6 7 14 15 22 23 30 31 67 --> 3 1 4 0 2 --> 0 8 2 10 16 24 18 26 1 9 3 11 17 25 19 27 4 12 6 14 20 28 22 30 5 13 7 15 21 29 23 31 82 --> 2 4 0 3 1 --> 0 4 16 20 1 5 17 21 8 12 24 28 9 13 25 29 2 6 18 22 3 7 19 23 10 14 26 30 11 15 27 31 86 --> 0 4 3 2 1 --> 0 1 16 17 8 9 24 25 4 5 20 21 12 13 28 29 2 3 18 19 10 11 26 27 6 7 22 23 14 15 30 31 94 --> 3 4 2 0 1 --> 0 8 16 24 4 12 20 28 1 9 17 25 5 13 21 29 2 10 18 26 6 14 22 30 3 11 19 27 7 15 23 31 107 --> 4 2 1 3 0 --> 0 16 4 20 2 18 6 22 8 24 12 28 10 26 14 30 1 17 5 21 3 19 7 23 9 25 13 29 11 27 15 31 111 --> 4 1 3 2 0 --> 0 16 2 18 8 24 10 26 4 20 6 22 12 28 14 30 1 17 3 19 9 25 11 27 5 21 7 23 13 29 15 31 119 --> 4 3 2 1 0 --> 0 16 8 24 4 20 12 28 2 18 10 26 6 22 14 30 1 17 9 25 5 21 13 29 3 19 11 27 7 23 15 31
9 --> 3 0 1 2 4 --> 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 15 16 18 20 22 24 26 28 30 17 19 21 23 25 27 29 31 10 --> 1 3 0 2 4 --> 0 4 1 5 8 12 9 13 2 6 3 7 10 14 11 15 16 20 17 21 24 28 25 29 18 22 19 23 26 30 27 31 13 --> 2 0 3 1 4 --> 0 2 8 10 1 3 9 11 4 6 12 14 5 7 13 15 16 18 24 26 17 19 25 27 20 22 28 30 21 23 29 31 17 --> 3 2 0 1 4 --> 0 4 8 12 2 6 10 14 1 5 9 13 3 7 11 15 16 20 24 28 18 22 26 30 17 21 25 29 19 23 27 31 18 --> 1 2 3 0 4 --> 0 8 1 9 2 10 3 11 4 12 5 13 6 14 7 15 16 24 17 25 18 26 19 27 20 28 21 29 22 30 23 31 22 --> 2 3 1 0 4 --> 0 8 4 12 1 9 5 13 2 10 6 14 3 11 7 15 16 24 20 28 17 25 21 29 18 26 22 30 19 27 23 31 32 --> 0 4 1 2 3 --> 0 1 4 5 8 9 12 13 16 17 20 21 24 25 28 29 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 31 35 --> 4 1 0 2 3 --> 0 4 2 6 8 12 10 14 16 20 18 22 24 28 26 30 1 5 3 7 9 13 11 15 17 21 19 23 25 29 27 31 36 --> 0 2 4 1 3 --> 0 1 8 9 2 3 10 11 16 17 24 25 18 19 26 27 4 5 12 13 6 7 14 15 20 21 28 29 22 23 30 31 39 --> 4 0 2 1 3 --> 0 2 8 10 4 6 12 14 16 18 24 26 20 22 28 30 1 3 9 11 5 7 13 15 17 19 25 27 21 23 29 31 43 --> 2 1 4 0 3 --> 0 8 2 10 1 9 3 11 16 24 18 26 17 25 19 27 4 12 6 14 5 13 7 15 20 28 22 30 21 29 23 31 44 --> 1 4 2 0 3 --> 0 8 1 9 4 12 5 13 16 24 17 25 20 28 21 29 2 10 3 11 6 14 7 15 18 26 19 27 22 30 23 31 50 --> 0 3 1 4 2 --> 0 1 4 5 16 17 20 21 2 3 6 7 18 19 22 23 8 9 12 13 24 25 28 29 10 11 14 15 26 27 30 31 53 --> 3 1 0 4 2 --> 0 4 2 6 16 20 18 22 1 5 3 7 17 21 19 23 8 12 10 14 24 28 26 30 9 13 11 15 25 29 27 31 57 --> 4 0 1 3 2 --> 0 2 4 6 16 18 20 22 8 10 12 14 24 26 28 30 1 3 5 7 17 19 21 23 9 11 13 15 25 27 29 31 58 --> 1 4 0 3 2 --> 0 4 1 5 16 20 17 21 8 12 9 13 24 28 25 29 2 6 3 7 18 22 19 23 10 14 11 15 26 30 27 31 62 --> 0 4 3 1 2 --> 0 1 8 9 16 17 24 25 4 5 12 13 20 21 28 29 2 3 10 11 18 19 26 27 6 7 14 15 22 23 30 31 69 --> 4 1 3 0 2 --> 0 8 2 10 16 24 18 26 4 12 6 14 20 28 22 30 1 9 3 11 17 25 19 27 5 13 7 15 21 29 23 31 72 --> 0 2 3 4 1 --> 0 1 16 17 2 3 18 19 4 5 20 21 6 7 22 23 8 9 24 25 10 11 26 27 12 13 28 29 14 15 30 31 75 --> 3 0 2 4 1 --> 0 2 16 18 4 6 20 22 1 3 17 19 5 7 21 23 8 10 24 26 12 14 28 30 9 11 25 27 13 15 29 31 79 --> 2 0 4 3 1 --> 0 2 16 18 1 3 17 19 8 10 24 26 9 11 25 27 4 6 20 22 5 7 21 23 12 14 28 30 13 15 29 31 83 --> 4 2 0 3 1 --> 0 4 16 20 2 6 18 22 8 12 24 28 10 14 26 30 1 5 17 21 3 7 19 23 9 13 25 29 11 15 27 31 84 --> 0 3 4 2 1 --> 0 1 16 17 8 9 24 25 2 3 18 19 10 11 26 27 4 5 20 21 12 13 28 29 6 7 22 23 14 15 30 31 95 --> 4 3 2 0 1 --> 0 8 16 24 4 12 20 28 2 10 18 26 6 14 22 30 1 9 17 25 5 13 21 29 3 11 19 27 7 15 23 31 97 --> 2 1 3 4 0 --> 0 16 2 18 1 17 3 19 4 20 6 22 5 21 7 23 8 24 10 26 9 25 11 27 12 28 14 30 13 29 15 31 98 --> 1 3 2 4 0 --> 0 16 1 17 4 20 5 21 2 18 3 19 6 22 7 23 8 24 9 25 12 28 13 29 10 26 11 27 14 30 15 31 102 --> 1 2 4 3 0 --> 0 16 1 17 2 18 3 19 8 24 9 25 10 26 11 27 4 20 5 21 6 22 7 23 12 28 13 29 14 30 15 31 106 --> 2 4 1 3 0 --> 0 16 4 20 1 17 5 21 8 24 12 28 9 25 13 29 2 18 6 22 3 19 7 23 10 26 14 30 11 27 15 31 109 --> 3 1 4 2 0 --> 0 16 2 18 8 24 10 26 1 17 3 19 9 25 11 27 4 20 6 22 12 28 14 30 5 21 7 23 13 29 15 31 118 --> 3 4 2 1 0 --> 0 16 8 24 4 20 12 28 1 17 9 25 5 21 13 29 2 18 10 26 6 22 14 30 3 19 11 27 7 23 15 31
27 --> 2 0 1 4 3 --> 0 2 4 6 1 3 5 7 16 18 20 22 17 19 21 23 8 10 12 14 9 11 13 15 24 26 28 30 25 27 29 31 28 --> 1 2 0 4 3 --> 0 4 1 5 2 6 3 7 16 20 17 21 18 22 19 23 8 12 9 13 10 14 11 15 24 28 25 29 26 30 27 31 31 --> 1 0 4 2 3 --> 0 2 1 3 8 10 9 11 16 18 17 19 24 26 25 27 4 6 5 7 12 14 13 15 20 22 21 23 28 30 29 31 40 --> 2 4 0 1 3 --> 0 4 8 12 1 5 9 13 16 20 24 28 17 21 25 29 2 6 10 14 3 7 11 15 18 22 26 30 19 23 27 31 47 --> 4 2 1 0 3 --> 0 8 4 12 2 10 6 14 16 24 20 28 18 26 22 30 1 9 5 13 3 11 7 15 17 25 21 29 19 27 23 31 49 --> 1 0 3 4 2 --> 0 2 1 3 16 18 17 19 4 6 5 7 20 22 21 23 8 10 9 11 24 26 25 27 12 14 13 15 28 30 29 31 61 --> 3 0 4 1 2 --> 0 2 8 10 16 18 24 26 1 3 9 11 17 19 25 27 4 6 12 14 20 22 28 30 5 7 13 15 21 23 29 31 65 --> 4 3 0 1 2 --> 0 4 8 12 16 20 24 28 2 6 10 14 18 22 26 30 1 5 9 13 17 21 25 29 3 7 11 15 19 23 27 31 66 --> 1 3 4 0 2 --> 0 8 1 9 16 24 17 25 2 10 3 11 18 26 19 27 4 12 5 13 20 28 21 29 6 14 7 15 22 30 23 31 70 --> 3 4 1 0 2 --> 0 8 4 12 16 24 20 28 1 9 5 13 17 25 21 29 2 10 6 14 18 26 22 30 3 11 7 15 19 27 23 31 76 --> 2 3 0 4 1 --> 0 4 16 20 1 5 17 21 2 6 18 22 3 7 19 23 8 12 24 28 9 13 25 29 10 14 26 30 11 15 27 31 87 --> 4 0 3 2 1 --> 0 2 16 18 8 10 24 26 4 6 20 22 12 14 28 30 1 3 17 19 9 11 25 27 5 7 21 23 13 15 29 31 88 --> 3 4 0 2 1 --> 0 4 16 20 8 12 24 28 1 5 17 21 9 13 25 29 2 6 18 22 10 14 26 30 3 7 19 23 11 15 27 31 91 --> 3 2 4 0 1 --> 0 8 16 24 2 10 18 26 1 9 17 25 3 11 19 27 4 12 20 28 6 14 22 30 5 13 21 29 7 15 23 31 92 --> 2 4 3 0 1 --> 0 8 16 24 1 9 17 25 4 12 20 28 5 13 21 29 2 10 18 26 3 11 19 27 6 14 22 30 7 15 23 31 101 --> 3 2 1 4 0 --> 0 16 4 20 2 18 6 22 1 17 5 21 3 19 7 23 8 24 12 28 10 26 14 30 9 25 13 29 11 27 15 31 110 --> 1 4 3 2 0 --> 0 16 1 17 8 24 9 25 4 20 5 21 12 28 13 29 2 18 3 19 10 26 11 27 6 22 7 23 14 30 15 31 113 --> 4 3 1 2 0 --> 0 16 4 20 8 24 12 28 2 18 6 22 10 26 14 30 1 17 5 21 9 25 13 29 3 19 7 23 11 27 15 31 114 --> 2 3 4 1 0 --> 0 16 8 24 1 17 9 25 2 18 10 26 3 19 11 27 4 20 12 28 5 21 13 29 6 22 14 30 7 23 15 31 117 --> 4 2 3 1 0 --> 0 16 8 24 2 18 10 26 4 20 12 28 6 22 14 30 1 17 9 25 3 19 11 27 5 21 13 29 7 23 15 31
33 --> 4 0 1 2 3 --> 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 34 --> 1 4 0 2 3 --> 0 4 1 5 8 12 9 13 16 20 17 21 24 28 25 29 2 6 3 7 10 14 11 15 18 22 19 23 26 30 27 31 37 --> 2 0 4 1 3 --> 0 2 8 10 1 3 9 11 16 18 24 26 17 19 25 27 4 6 12 14 5 7 13 15 20 22 28 30 21 23 29 31 41 --> 4 2 0 1 3 --> 0 4 8 12 2 6 10 14 16 20 24 28 18 22 26 30 1 5 9 13 3 7 11 15 17 21 25 29 19 23 27 31 42 --> 1 2 4 0 3 --> 0 8 1 9 2 10 3 11 16 24 17 25 18 26 19 27 4 12 5 13 6 14 7 15 20 28 21 29 22 30 23 31 46 --> 2 4 1 0 3 --> 0 8 4 12 1 9 5 13 16 24 20 28 17 25 21 29 2 10 6 14 3 11 7 15 18 26 22 30 19 27 23 31 51 --> 3 0 1 4 2 --> 0 2 4 6 16 18 20 22 1 3 5 7 17 19 21 23 8 10 12 14 24 26 28 30 9 11 13 15 25 27 29 31 52 --> 1 3 0 4 2 --> 0 4 1 5 16 20 17 21 2 6 3 7 18 22 19 23 8 12 9 13 24 28 25 29 10 14 11 15 26 30 27 31 63 --> 4 0 3 1 2 --> 0 2 8 10 16 18 24 26 4 6 12 14 20 22 28 30 1 3 9 11 17 19 25 27 5 7 13 15 21 23 29 31 64 --> 3 4 0 1 2 --> 0 4 8 12 16 20 24 28 1 5 9 13 17 21 25 29 2 6 10 14 18 22 26 30 3 7 11 15 19 23 27 31 68 --> 1 4 3 0 2 --> 0 8 1 9 16 24 17 25 4 12 5 13 20 28 21 29 2 10 3 11 18 26 19 27 6 14 7 15 22 30 23 31 71 --> 4 3 1 0 2 --> 0 8 4 12 16 24 20 28 2 10 6 14 18 26 22 30 1 9 5 13 17 25 21 29 3 11 7 15 19 27 23 31 73 --> 2 0 3 4 1 --> 0 2 16 18 1 3 17 19 4 6 20 22 5 7 21 23 8 10 24 26 9 11 25 27 12 14 28 30 13 15 29 31 77 --> 3 2 0 4 1 --> 0 4 16 20 2 6 18 22 1 5 17 21 3 7 19 23 8 12 24 28 10 14 26 30 9 13 25 29 11 15 27 31 85 --> 3 0 4 2 1 --> 0 2 16 18 8 10 24 26 1 3 17 19 9 11 25 27 4 6 20 22 12 14 28 30 5 7 21 23 13 15 29 31 89 --> 4 3 0 2 1 --> 0 4 16 20 8 12 24 28 2 6 18 22 10 14 26 30 1 5 17 21 9 13 25 29 3 7 19 23 11 15 27 31 90 --> 2 3 4 0 1 --> 0 8 16 24 1 9 17 25 2 10 18 26 3 11 19 27 4 12 20 28 5 13 21 29 6 14 22 30 7 15 23 31 93 --> 4 2 3 0 1 --> 0 8 16 24 2 10 18 26 4 12 20 28 6 14 22 30 1 9 17 25 3 11 19 27 5 13 21 29 7 15 23 31 96 --> 1 2 3 4 0 --> 0 16 1 17 2 18 3 19 4 20 5 21 6 22 7 23 8 24 9 25 10 26 11 27 12 28 13 29 14 30 15 31 100 --> 2 3 1 4 0 --> 0 16 4 20 1 17 5 21 2 18 6 22 3 19 7 23 8 24 12 28 9 25 13 29 10 26 14 30 11 27 15 31 108 --> 1 3 4 2 0 --> 0 16 1 17 8 24 9 25 2 18 3 19 10 26 11 27 4 20 5 21 12 28 13 29 6 22 7 23 14 30 15 31 112 --> 3 4 1 2 0 --> 0 16 4 20 8 24 12 28 1 17 5 21 9 25 13 29 2 18 6 22 10 26 14 30 3 19 7 23 11 27 15 31 115 --> 3 2 4 1 0 --> 0 16 8 24 2 18 10 26 1 17 9 25 3 19 11 27 4 20 12 28 6 22 14 30 5 21 13 29 7 23 15 31 116 --> 2 4 3 1 0 --> 0 16 8 24 1 17 9 25 4 20 12 28 5 21 13 29 2 18 10 26 3 19 11 27 6 22 14 30 7 23 15 31 |
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