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A280319 Irregular triangle read by rows: T(m, n) is the n-th permutation of m things generated by the Steinhaus-Johnson-Trotter algorithm, represented by row number of A055089. 2
0, 0, 1, 0, 2, 3, 5, 4, 1, 0, 6, 8, 9, 15, 14, 12, 2, 3, 13, 16, 17, 23, 22, 19, 5, 4, 18, 20, 21, 11, 10, 7, 1, 0, 24, 30, 32, 33, 57, 56, 54, 48, 6, 8, 50, 60, 62, 63, 65, 64, 61, 51, 9, 15, 75, 85, 88, 89, 87, 86, 84, 74, 14, 12, 72, 78, 80, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row m is a permutation of the integers 0..m!-1, so this is a triangle in which row m>=1 has length A000142(m):

m/n   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

1     0

2     0  1

3     0  2  3  5  4  1

4     0  6  8  9 15 14 12  2  3 13 16 17 23 22 19  5  4 18 20 21 11 10  7  1

Compare A280318 for Heap's algorithm, which is one infinite permutation rather than a triangle of finite permutations.

LINKS

Tilman Piesk, Triangle rows m=1..7, flattened

Tilman Piesk, Calculation with Python

Wikipedia, Steinhaus-Johnson-Trotter algorithm

EXAMPLE

Example for row m=4. On the right are the permutations of {1,2,3,4} in the order generated by the Steinhaus-Johnson-Trotter algorithm:

   n    rev colex      T(4,n)     SJT

   0     1 2 3 4          0     1 2 3 4

   1     2 1 3 4          6     1 2 4 3

   2     1 3 2 4          8     1 4 2 3

   3     3 1 2 4          9     4 1 2 3

   4     2 3 1 4         15     4 1 3 2

   5     3 2 1 4         14     1 4 3 2

   6     1 2 4 3         12     1 3 4 2

   7     2 1 4 3          2     1 3 2 4

   8     1 4 2 3          3     3 1 2 4

   9     4 1 2 3         13     3 1 4 2

  10     2 4 1 3         16     3 4 1 2

  11     4 2 1 3         17     4 3 1 2

  12     1 3 4 2         23     4 3 2 1

  13     3 1 4 2         22     3 4 2 1

  14     1 4 3 2         19     3 2 4 1

  15     4 1 3 2          5     3 2 1 4

  16     3 4 1 2          4     2 3 1 4

  17     4 3 1 2         18     2 3 4 1

  18     2 3 4 1         20     2 4 3 1

  19     3 2 4 1         21     4 2 3 1

  20     2 4 3 1         11     4 2 1 3

  21     4 2 3 1         10     2 4 1 3

  22     3 4 2 1          7     2 1 4 3

  23     4 3 2 1          1     2 1 3 4

CROSSREFS

Cf. A000142, A055089, A280318.

Sequence in context: A060444 A002587 A152814 * A021981 A281941 A284278

Adjacent sequences:  A280316 A280317 A280318 * A280320 A280321 A280322

KEYWORD

nonn,tabf

AUTHOR

Tilman Piesk, Dec 31 2016

STATUS

approved

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Last modified October 18 01:39 EDT 2021. Contains 348065 sequences. (Running on oeis4.)