A275078 Triangle read by rows in which row n lists the lexicographic composition of the elements of symmetric group S_n.

1, 2, 1, 2, 1, 3, 3, 4, 1, 2, 2, 4, 1, 5, 3, 5, 4, 2, 6, 1, 3, 4, 7, 5, 1, 3, 2, 6, 8, 1, 2, 3, 4, 7, 6, 5, 6, 9, 2, 1, 7, 8, 5, 4, 3, 2, 8, 9, 4, 6, 7, 10, 5, 1, 3, 5, 1, 6, 10, 8, 11, 9, 2, 7, 3, 4, 7, 1, 9, 5, 6, 2, 12, 4, 8, 11, 10, 3

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Example

Triangle begins:
1
2  1
2  1  3
3  4  1  2
2  4  1  5  3
5  4  2  6  1  3
4  7  5  1  3  2  6
8  1  2  3  4  7  6  5
6  9  2  1  7  8  5  4  3
2  8  9  4  6  7  10 5  1  3
5  1  6  10 8  11 9  2  7  3  4
7  1  9  5  6  2  12 4  8  11 10  3
For the third row, the 6 permutations of 123 in lexical order are 123, 132, 213, 231, 312, and 321. Consecutively applying each permutation to 123 results in the sequence: 123, 132, 312, 123, 312, 213. The final element with commas inserted gives us the row: 2,1,3.

Prog

(Python)
from itertools import count, permutations
for size in count(1):
    row = tuple(range(1, size + 1))
    for p in permutations(range(size)):
        row = tuple(row[i] for i in p)
    print(row)

Crossrefs

Sequence in context: A318362 A213237 A029334 * A286478 A340756 A030273

Adjacent sequences: A275075 A275076 A275077 * A275079 A275080 A275081

Keyword

nonn,tabl

Author

David Nickerson, Jul 15 2016

Status

approved