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A211364 Inversion sets of finite permutations that have only 0's and 1's in their inversion vectors.

%I A211364 #17 Apr 05 2020 21:29:16
%S A211364 0,1,4,3,32,33,20,11,512,513,516,515,288,289,148,75,16384,16385,16388,
%T A211364 16387,16416,16417,16404,16395,8704,8705,8708,8707,4384,4385,2196,
%U A211364 1099,1048576,1048577,1048580,1048579,1048608,1048609,1048596
%N A211364 Inversion sets of finite permutations that have only 0's and 1's in their inversion vectors.
%C A211364 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 A211364 Tilman Piesk, <a href="/A211364/b211364.txt">Table of n, a(n) for n = 0..127</a>
%F A211364 a(n) =  A211362(A059590(n)).
%e A211364 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 A211364 No.  permutation  inv. vector  inversion set     a
%e A211364 00     1 2 3 4     0 0 0 0     0  0 0  0 0 0     0
%e A211364 01     2 1 3 4     0 1 0 0     1  0 0  0 0 0     1
%e A211364 02     1 3 2 4     0 0 1 0     0  0 1  0 0 0     4
%e A211364 03     3 1 2 4     0 1 1 0     1  1 0  0 0 0     3
%e A211364 06     1 2 4 3     0 0 0 1     0  0 0  0 0 1    32
%e A211364 07     2 1 4 3     0 1 0 1     1  0 0  0 0 1    33
%e A211364 08     1 4 2 3     0 0 1 1     0  0 1  0 1 0    20
%e A211364 09     4 1 2 3     0 1 1 1     1  1 0  1 0 0    11
%Y A211364 Cf. A211362, A059590.
%K A211364 nonn
%O A211364 0,3
%A A211364 _Tilman Piesk_, Jun 03 2012