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

0, 1, 4, 3, 32, 33, 20, 11, 512, 513, 516, 515, 288, 289, 148, 75, 16384, 16385, 16388, 16387, 16416, 16417, 16404, 16395, 8704, 8705, 8708, 8707, 4384, 4385, 2196, 1099, 1048576, 1048577, 1048580, 1048579, 1048608, 1048609, 1048596

Offset

0,3

Comments

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).

Links

Tilman Piesk, Table of n, a(n) for n = 0..127

Formula

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

Example

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.
No.  permutation  inv. vector  inversion set     a
00     1 2 3 4     0 0 0 0     0  0 0  0 0 0     0
01     2 1 3 4     0 1 0 0     1  0 0  0 0 0     1
02     1 3 2 4     0 0 1 0     0  0 1  0 0 0     4
03     3 1 2 4     0 1 1 0     1  1 0  0 0 0     3
06     1 2 4 3     0 0 0 1     0  0 0  0 0 1    32
07     2 1 4 3     0 1 0 1     1  0 0  0 0 1    33
08     1 4 2 3     0 0 1 1     0  0 1  0 1 0    20
09     4 1 2 3     0 1 1 1     1  1 0  1 0 0    11

Crossrefs

Cf. A211362, A059590.

Sequence in context: A286795 A127138 A064081 * A099438 A002178 A013558

Adjacent sequences: A211361 A211362 A211363 * A211365 A211366 A211367

Keyword

nonn

Author

Tilman Piesk, Jun 03 2012

Status

approved