A211363 Permutation corresponding to the inversion sets interpreted as binary numbers (A211362) ordered by value.

0, 1, 3, 2, 4, 5, 9, 11, 8, 10, 16, 17, 6, 7, 13, 15, 12, 14, 18, 19, 21, 20, 22, 23, 33, 35, 41, 39, 45, 47, 32, 34, 40, 38, 44, 46, 64, 65, 70, 71, 30, 31, 37, 36, 42, 43, 61, 63, 67, 69, 60, 62, 66, 68, 90, 91, 93, 92, 94, 95, 24, 25, 27

Offset

0,3

Comments

A211362 lists the binary interpretations of inversion sets ordered by the reverse colexicographic order of permutations (A055089). This permutation orders them by value. Its inverse begins: 0, 1, 3, 2, 4, 5, 12, 13, 8, 6, 9, 7, 16, 14, 17, 15, 10, 11, 18, 19, 21, 20, 22, 23, ...

Links

Tilman Piesk, Table of n, a(n) for n = 0..5039

Index entries for sequences related to factorial base representation

Example

These are the first 24 finite permutations. The inversion sets interpreted as binary numbers on the right form the sequence A211362, which is not monotonic:
No.  permutation   inversion set  A211362
00     1 2 3 4     0  0 0  0 0 0     0
01     2 1 3 4     1  0 0  0 0 0     1
02     1 3 2 4     0  0 1  0 0 0     4
03     3 1 2 4     1  1 0  0 0 0     3
04     2 3 1 4     0  1 1  0 0 0     6
05     3 2 1 4     1  1 1  0 0 0     7
06     1 2 4 3     0  0 0  0 0 1    32
07     2 1 4 3     1  0 0  0 0 1    33
08     1 4 2 3     0  0 1  0 1 0    20
09     4 1 2 3     1  1 0  1 0 0    11
10     2 4 1 3     0  1 1  0 1 0    22
11     4 2 1 3     1  1 1  1 0 0    15
12     1 3 4 2     0  0 0  0 1 1    48
13     3 1 4 2     1  0 0  1 0 1    41
14     1 4 3 2     0  0 1  0 1 1    52
15     4 1 3 2     1  1 0  1 0 1    43
16     3 4 1 2     0  1 1  1 1 0    30
17     4 3 1 2     1  1 1  1 1 0    31
18     2 3 4 1     0  0 0  1 1 1    56
19     3 2 4 1     1  0 0  1 1 1    57
20     2 4 3 1     0  0 1  1 1 1    60
21     4 2 3 1     1  1 0  1 1 1    59
22     3 4 2 1     0  1 1  1 1 1    62
23     4 3 2 1     1  1 1  1 1 1    63
This is the same list ordered by the inversion sets, so the right column is monotonic now. The left column is the beginning of the permutation p, i.e., this sequence:
No.  permutation   inversion set  A211362*p
00     1 2 3 4     0  0 0  0 0 0     0
01     2 1 3 4     1  0 0  0 0 0     1
03     3 1 2 4     1  1 0  0 0 0     3
02     1 3 2 4     0  0 1  0 0 0     4
04     2 3 1 4     0  1 1  0 0 0     6
05     3 2 1 4     1  1 1  0 0 0     7
09     4 1 2 3     1  1 0  1 0 0    11
11     4 2 1 3     1  1 1  1 0 0    15
08     1 4 2 3     0  0 1  0 1 0    20
10     2 4 1 3     0  1 1  0 1 0    22
16     3 4 1 2     0  1 1  1 1 0    30
17     4 3 1 2     1  1 1  1 1 0    31
06     1 2 4 3     0  0 0  0 0 1    32
07     2 1 4 3     1  0 0  0 0 1    33
13     3 1 4 2     1  0 0  1 0 1    41
15     4 1 3 2     1  1 0  1 0 1    43
12     1 3 4 2     0  0 0  0 1 1    48
14     1 4 3 2     0  0 1  0 1 1    52
18     2 3 4 1     0  0 0  1 1 1    56
19     3 2 4 1     1  0 0  1 1 1    57
21     4 2 3 1     1  1 0  1 1 1    59
20     2 4 3 1     0  0 1  1 1 1    60
22     3 4 2 1     0  1 1  1 1 1    62
23     4 3 2 1     1  1 1  1 1 1    63

Crossrefs

Cf. A211362.

Sequence in context: A305369 A097092 A241417 * A059320 A334792 A255167

Adjacent sequences: A211360 A211361 A211362 * A211364 A211365 A211366

Keyword

nonn,base,look

Author

Tilman Piesk, Jun 03 2012

Status

approved