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 A211363 Permutation corresponding to the inversion sets interpreted as binary numbers (A211362) ordered by value. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 00     1 2 3 4     0  0 0  0 0 0     0 01     2 1 3 4     1  0 0  0 0 0     1 03     3 1 2 4     1  1 0  0 0 0     3 02     1 3 2 4     0  0 1  0 0 0     4 04     2 3 1 4     0  1 1  0 0 0     6 05     3 2 1 4     1  1 1  0 0 0     7 09     4 1 2 3     1  1 0  1 0 0    11 11     4 2 1 3     1  1 1  1 0 0    15 08     1 4 2 3     0  0 1  0 1 0    20 10     2 4 1 3     0  1 1  0 1 0    22 16     3 4 1 2     0  1 1  1 1 0    30 17     4 3 1 2     1  1 1  1 1 0    31 06     1 2 4 3     0  0 0  0 0 1    32 07     2 1 4 3     1  0 0  0 0 1    33 13     3 1 4 2     1  0 0  1 0 1    41 15     4 1 3 2     1  1 0  1 0 1    43 12     1 3 4 2     0  0 0  0 1 1    48 14     1 4 3 2     0  0 1  0 1 1    52 18     2 3 4 1     0  0 0  1 1 1    56 19     3 2 4 1     1  0 0  1 1 1    57 21     4 2 3 1     1  1 0  1 1 1    59 20     2 4 3 1     0  0 1  1 1 1    60 22     3 4 2 1     0  1 1  1 1 1    62 23     4 3 2 1     1  1 1  1 1 1    63 CROSSREFS Cf. A211362. Sequence in context: A305369 A097092 A241417 * A059320 A334792 A255167 Adjacent sequences:  A211360 A211361 A211362 * A211364 A211365 A211366 KEYWORD nonn,base,look AUTHOR Tilman Piesk, Jun 03 2012 STATUS approved

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Last modified January 23 16:29 EST 2022. Contains 350514 sequences. (Running on oeis4.)