A211363 - OEIS

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

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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