Identifier
Values
0 => 0 => [2] => 0
1 => 1 => [1,1] => 0
00 => 00 => [3] => 0
01 => 01 => [2,1] => 0
10 => 01 => [2,1] => 0
11 => 11 => [1,1,1] => 0
000 => 000 => [4] => 0
001 => 001 => [3,1] => 0
010 => 001 => [3,1] => 0
011 => 011 => [2,1,1] => 0
100 => 001 => [3,1] => 0
101 => 011 => [2,1,1] => 0
110 => 011 => [2,1,1] => 0
111 => 111 => [1,1,1,1] => 0
0000 => 0000 => [5] => 0
0001 => 0001 => [4,1] => 0
0010 => 0001 => [4,1] => 0
0011 => 0011 => [3,1,1] => 0
0100 => 0001 => [4,1] => 0
0101 => 0101 => [2,2,1] => 0
0110 => 0011 => [3,1,1] => 0
0111 => 0111 => [2,1,1,1] => 0
1000 => 0001 => [4,1] => 0
1001 => 0011 => [3,1,1] => 0
1010 => 0011 => [3,1,1] => 0
1011 => 0111 => [2,1,1,1] => 0
1100 => 0011 => [3,1,1] => 0
1101 => 0111 => [2,1,1,1] => 0
1110 => 0111 => [2,1,1,1] => 0
1111 => 1111 => [1,1,1,1,1] => 0
00000 => 00000 => [6] => 0
00001 => 00001 => [5,1] => 0
00010 => 00001 => [5,1] => 0
00011 => 00011 => [4,1,1] => 0
00100 => 00001 => [5,1] => 0
00101 => 00101 => [3,2,1] => 0
00110 => 00011 => [4,1,1] => 0
00111 => 00111 => [3,1,1,1] => 0
01000 => 00001 => [5,1] => 0
01001 => 00101 => [3,2,1] => 0
01010 => 00101 => [3,2,1] => 0
01011 => 01011 => [2,2,1,1] => 0
01100 => 00011 => [4,1,1] => 0
01101 => 01011 => [2,2,1,1] => 0
01110 => 00111 => [3,1,1,1] => 0
01111 => 01111 => [2,1,1,1,1] => 0
10000 => 00001 => [5,1] => 0
10001 => 00011 => [4,1,1] => 0
10010 => 00011 => [4,1,1] => 0
10011 => 00111 => [3,1,1,1] => 0
10100 => 00011 => [4,1,1] => 0
10101 => 01011 => [2,2,1,1] => 0
10110 => 00111 => [3,1,1,1] => 0
10111 => 01111 => [2,1,1,1,1] => 0
11000 => 00011 => [4,1,1] => 0
11001 => 00111 => [3,1,1,1] => 0
11010 => 00111 => [3,1,1,1] => 0
11011 => 01111 => [2,1,1,1,1] => 0
11100 => 00111 => [3,1,1,1] => 0
11101 => 01111 => [2,1,1,1,1] => 0
11110 => 01111 => [2,1,1,1,1] => 0
11111 => 11111 => [1,1,1,1,1,1] => 0
000000 => 000000 => [7] => 0
000001 => 000001 => [6,1] => 0
000010 => 000001 => [6,1] => 0
000011 => 000011 => [5,1,1] => 0
000100 => 000001 => [6,1] => 0
000101 => 000101 => [4,2,1] => 0
000110 => 000011 => [5,1,1] => 0
000111 => 000111 => [4,1,1,1] => 0
001000 => 000001 => [6,1] => 0
001001 => 001001 => [3,3,1] => 0
001010 => 000101 => [4,2,1] => 0
001011 => 001011 => [3,2,1,1] => 0
001100 => 000011 => [5,1,1] => 0
001101 => 001101 => [3,1,2,1] => 1
001110 => 000111 => [4,1,1,1] => 0
001111 => 001111 => [3,1,1,1,1] => 0
010000 => 000001 => [6,1] => 0
010001 => 000101 => [4,2,1] => 0
010010 => 000101 => [4,2,1] => 0
010011 => 001101 => [3,1,2,1] => 1
010100 => 000101 => [4,2,1] => 0
010101 => 010101 => [2,2,2,1] => 0
010110 => 001011 => [3,2,1,1] => 0
010111 => 010111 => [2,2,1,1,1] => 0
011000 => 000011 => [5,1,1] => 0
011001 => 001011 => [3,2,1,1] => 0
011010 => 001011 => [3,2,1,1] => 0
011011 => 011011 => [2,1,2,1,1] => 1
011100 => 000111 => [4,1,1,1] => 0
011101 => 010111 => [2,2,1,1,1] => 0
011110 => 001111 => [3,1,1,1,1] => 0
011111 => 011111 => [2,1,1,1,1,1] => 0
100000 => 000001 => [6,1] => 0
100001 => 000011 => [5,1,1] => 0
100010 => 000011 => [5,1,1] => 0
100011 => 000111 => [4,1,1,1] => 0
100100 => 000011 => [5,1,1] => 0
100101 => 001011 => [3,2,1,1] => 0
100110 => 000111 => [4,1,1,1] => 0
>>> Load all 127 entries. <<<
100111 => 001111 => [3,1,1,1,1] => 0
101000 => 000011 => [5,1,1] => 0
101001 => 001011 => [3,2,1,1] => 0
101010 => 001011 => [3,2,1,1] => 0
101011 => 010111 => [2,2,1,1,1] => 0
101100 => 000111 => [4,1,1,1] => 0
101101 => 010111 => [2,2,1,1,1] => 0
101110 => 001111 => [3,1,1,1,1] => 0
101111 => 011111 => [2,1,1,1,1,1] => 0
110000 => 000011 => [5,1,1] => 0
110001 => 000111 => [4,1,1,1] => 0
110010 => 000111 => [4,1,1,1] => 0
110011 => 001111 => [3,1,1,1,1] => 0
110100 => 000111 => [4,1,1,1] => 0
110101 => 010111 => [2,2,1,1,1] => 0
110110 => 001111 => [3,1,1,1,1] => 0
110111 => 011111 => [2,1,1,1,1,1] => 0
111000 => 000111 => [4,1,1,1] => 0
111001 => 001111 => [3,1,1,1,1] => 0
111010 => 001111 => [3,1,1,1,1] => 0
111011 => 011111 => [2,1,1,1,1,1] => 0
111100 => 001111 => [3,1,1,1,1] => 0
111101 => 011111 => [2,1,1,1,1,1] => 0
111110 => 011111 => [2,1,1,1,1,1] => 0
111111 => 111111 => [1,1,1,1,1,1,1] => 0
=> => [1] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The descent variation of a composition.
Defined in [1].
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.