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.

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

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).

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

Triangle begins:
  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
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 (A207324):
   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, A207324, 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