Identifier
Values
[1,0] => 10 => 01 => 00 => 2
[1,0,1,0] => 1010 => 0101 => 0000 => 4
[1,1,0,0] => 1100 => 0011 => 0110 => 2
[1,0,1,0,1,0] => 101010 => 010101 => 000000 => 6
[1,0,1,1,0,0] => 101100 => 001101 => 011000 => 3
[1,1,0,0,1,0] => 110010 => 010011 => 000110 => 3
[1,1,0,1,0,0] => 110100 => 001011 => 011110 => 4
[1,1,1,0,0,0] => 111000 => 000111 => 010010 => 2
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 00000000 => 8
[1,0,1,0,1,1,0,0] => 10101100 => 00110101 => 01100000 => 5
[1,0,1,1,0,0,1,0] => 10110010 => 01001101 => 00011000 => 3
[1,0,1,1,0,1,0,0] => 10110100 => 00101101 => 01111000 => 4
[1,0,1,1,1,0,0,0] => 10111000 => 00011101 => 01001000 => 3
[1,1,0,0,1,0,1,0] => 11001010 => 01010011 => 00000110 => 5
[1,1,0,0,1,1,0,0] => 11001100 => 00110011 => 01100110 => 2
[1,1,0,1,0,0,1,0] => 11010010 => 01001011 => 00011110 => 4
[1,1,0,1,0,1,0,0] => 11010100 => 00101011 => 01111110 => 6
[1,1,0,1,1,0,0,0] => 11011000 => 00011011 => 01001110 => 3
[1,1,1,0,0,0,1,0] => 11100010 => 01000111 => 00010010 => 3
[1,1,1,0,0,1,0,0] => 11100100 => 00100111 => 01110010 => 3
[1,1,1,0,1,0,0,0] => 11101000 => 00010111 => 01000010 => 4
[1,1,1,1,0,0,0,0] => 11110000 => 00001111 => 01011010 => 2
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0101010101 => 0000000000 => 10
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0100110101 => 0001100000 => 5
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0101001101 => 0000011000 => 5
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0100101101 => 0001111000 => 4
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0100011101 => 0001001000 => 3
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0101010011 => 0000000110 => 7
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0100110011 => 0001100110 => 3
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0101001011 => 0000011110 => 5
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0100101011 => 0001111110 => 6
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0100011011 => 0001001110 => 3
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0101000111 => 0000010010 => 5
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0100100111 => 0001110010 => 3
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0100010111 => 0001000010 => 4
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 0001010111 => 0100000010 => 6
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0100001111 => 0001011010 => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 001010110101 => 011111100000 => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 001011001101 => 011110011000 => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 001100101101 => 011001111000 => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 010010101101 => 000111111000 => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 000110101101 => 010011111000 => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 001001101101 => 011100111000 => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 000011101101 => 010110111000 => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 001010011101 => 011111001000 => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 001000111101 => 011101101000 => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 000010111101 => 010111101000 => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 001011010011 => 011110000110 => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 001100110011 => 011001100110 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 010010110011 => 000111100110 => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 001001110011 => 011100100110 => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 000011110011 => 010110100110 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 010100101011 => 000001111110 => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 010010011011 => 000111001110 => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 010000111011 => 000101101110 => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 001011000111 => 011110010010 => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 001100100111 => 011001110010 => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 010010100111 => 000111110010 => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 000110100111 => 010011110010 => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 001001100111 => 011100110010 => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 000011100111 => 010110110010 => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 001010010111 => 011111000010 => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 001000110111 => 011101100010 => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 000010110111 => 010111100010 => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 001100001111 => 011001011010 => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 010010001111 => 000111011010 => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 000110001111 => 010011011010 => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 001001001111 => 011100011010 => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 000011001111 => 010110011010 => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 010000101111 => 000101111010 => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 000100101111 => 010001111010 => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 001000011111 => 011101001010 => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 000010011111 => 010111001010 => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 000000111111 => 010101101010 => 2
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
click to show known generating functions       
Description
The length of the longest constant subword.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.
Map
reverse
Description
Return the reversal of a binary word.