%I #17 Apr 05 2020 21:29:16

%S 0,1,4,3,32,33,20,11,512,513,516,515,288,289,148,75,16384,16385,16388,

%T 16387,16416,16417,16404,16395,8704,8705,8708,8707,4384,4385,2196,

%U 1099,1048576,1048577,1048580,1048579,1048608,1048609,1048596

%N Inversion sets of finite permutations that have only 0's and 1's in their inversion vectors.

%C The finite permutations whose position in reverse colexicographic order is A059590(n) (compare A055089, A195663) have the special feature that their inversion vectors (compare A007623) have only zeros and ones, and give 2*n when interpreted as binary numbers. As the inversion vectors are special, one may also take a look at the inversion sets. This sequence shows them, interpreted as binary numbers (compare A211362).

%H Tilman Piesk, <a href="/A211364/b211364.txt">Table of n, a(n) for n = 0..127</a>

%F a(n) = A211362(A059590(n)).

%e These are the 8 permutations of 4 elements that have only 0's and 1's in their inversion vectors. The left column shows their numbers (compare A055089, A195663), i.e., the beginning of A059590. The right column shows the inversion sets interpreted as binary numbers, i.e., the beginning of this sequence.

%e No. permutation inv. vector inversion set a

%e 00 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0

%e 01 2 1 3 4 0 1 0 0 1 0 0 0 0 0 1

%e 02 1 3 2 4 0 0 1 0 0 0 1 0 0 0 4

%e 03 3 1 2 4 0 1 1 0 1 1 0 0 0 0 3

%e 06 1 2 4 3 0 0 0 1 0 0 0 0 0 1 32

%e 07 2 1 4 3 0 1 0 1 1 0 0 0 0 1 33

%e 08 1 4 2 3 0 0 1 1 0 0 1 0 1 0 20

%e 09 4 1 2 3 0 1 1 1 1 1 0 1 0 0 11

%Y Cf. A211362, A059590.

%K nonn

%O 0,3

%A _Tilman Piesk_, Jun 03 2012