A275078 - OEIS

%I #6 Aug 25 2016 21:01:03

%S 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,

%T 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,

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

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

%e Triangle begins:

%e 1

%e 2  1

%e 2  1  3

%e 3  4  1  2

%e 2  4  1  5  3

%e 5  4  2  6  1  3

%e 4  7  5  1  3  2  6

%e 8  1  2  3  4  7  6  5

%e 6  9  2  1  7  8  5  4  3

%e 2  8  9  4  6  7  10 5  1  3

%e 5  1  6  10 8  11 9  2  7  3  4

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

%e 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.

%o (Python)

%o from itertools import count, permutations

%o for size in count(1):

%o     row = tuple(range(1, size + 1))

%o     for p in permutations(range(size)):

%o         row = tuple(row[i] for i in p)

%o     print(row)

%K nonn,tabl

%O 1,2

%A _David Nickerson_, Jul 15 2016