%I
%S 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,
%T 41,39,45,47,32,34,40,38,44,46,64,65,70,71,30,31,37,36,42,43,61,63,67,
%U 69,60,62,66,68,90,91,93,92,94,95,24,25,27
%N Permutation corresponding to the inversion sets interpreted as binary numbers (A211362) ordered by value.
%C 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, ...
%H Tilman Piesk, <a href="/A211363/b211363.txt">Table of n, a(n) for n = 0..5039</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e 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:
%e No. permutation inversion set A211362
%e 00 1 2 3 4 0 0 0 0 0 0 0
%e 01 2 1 3 4 1 0 0 0 0 0 1
%e 02 1 3 2 4 0 0 1 0 0 0 4
%e 03 3 1 2 4 1 1 0 0 0 0 3
%e 04 2 3 1 4 0 1 1 0 0 0 6
%e 05 3 2 1 4 1 1 1 0 0 0 7
%e 06 1 2 4 3 0 0 0 0 0 1 32
%e 07 2 1 4 3 1 0 0 0 0 1 33
%e 08 1 4 2 3 0 0 1 0 1 0 20
%e 09 4 1 2 3 1 1 0 1 0 0 11
%e 10 2 4 1 3 0 1 1 0 1 0 22
%e 11 4 2 1 3 1 1 1 1 0 0 15
%e 12 1 3 4 2 0 0 0 0 1 1 48
%e 13 3 1 4 2 1 0 0 1 0 1 41
%e 14 1 4 3 2 0 0 1 0 1 1 52
%e 15 4 1 3 2 1 1 0 1 0 1 43
%e 16 3 4 1 2 0 1 1 1 1 0 30
%e 17 4 3 1 2 1 1 1 1 1 0 31
%e 18 2 3 4 1 0 0 0 1 1 1 56
%e 19 3 2 4 1 1 0 0 1 1 1 57
%e 20 2 4 3 1 0 0 1 1 1 1 60
%e 21 4 2 3 1 1 1 0 1 1 1 59
%e 22 3 4 2 1 0 1 1 1 1 1 62
%e 23 4 3 2 1 1 1 1 1 1 1 63
%e 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:
%e No. permutation inversion set A211362*p
%e 00 1 2 3 4 0 0 0 0 0 0 0
%e 01 2 1 3 4 1 0 0 0 0 0 1
%e 03 3 1 2 4 1 1 0 0 0 0 3
%e 02 1 3 2 4 0 0 1 0 0 0 4
%e 04 2 3 1 4 0 1 1 0 0 0 6
%e 05 3 2 1 4 1 1 1 0 0 0 7
%e 09 4 1 2 3 1 1 0 1 0 0 11
%e 11 4 2 1 3 1 1 1 1 0 0 15
%e 08 1 4 2 3 0 0 1 0 1 0 20
%e 10 2 4 1 3 0 1 1 0 1 0 22
%e 16 3 4 1 2 0 1 1 1 1 0 30
%e 17 4 3 1 2 1 1 1 1 1 0 31
%e 06 1 2 4 3 0 0 0 0 0 1 32
%e 07 2 1 4 3 1 0 0 0 0 1 33
%e 13 3 1 4 2 1 0 0 1 0 1 41
%e 15 4 1 3 2 1 1 0 1 0 1 43
%e 12 1 3 4 2 0 0 0 0 1 1 48
%e 14 1 4 3 2 0 0 1 0 1 1 52
%e 18 2 3 4 1 0 0 0 1 1 1 56
%e 19 3 2 4 1 1 0 0 1 1 1 57
%e 21 4 2 3 1 1 1 0 1 1 1 59
%e 20 2 4 3 1 0 0 1 1 1 1 60
%e 22 3 4 2 1 0 1 1 1 1 1 62
%e 23 4 3 2 1 1 1 1 1 1 1 63
%Y Cf. A211362.
%K nonn,base,look
%O 0,3
%A _Tilman Piesk_, Jun 03 2012
