login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A211363
Permutation corresponding to the inversion sets interpreted as binary numbers (A211362) ordered by value.
2
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, ...
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 * A376901 A059320 A334792
KEYWORD
nonn,base,look
AUTHOR
Tilman Piesk, Jun 03 2012
STATUS
approved