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

Author

Tilman Piesk, Jun 03 2012

Keywords

• nonn
• base
• look

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, ...

Examples

			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
		

Links

• Tilman Piesk, Table of n, a(n) for n = 0..5039
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A211362.