Identifier
-
Mp00093:
Dyck paths
—to binary word⟶
Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
St000982: Binary words ⟶ ℤ
Values
[1,0] => 10 => 01 => 10 => 1
[1,0,1,0] => 1010 => 0101 => 1010 => 1
[1,1,0,0] => 1100 => 0110 => 0011 => 2
[1,0,1,0,1,0] => 101010 => 010101 => 101010 => 1
[1,0,1,1,0,0] => 101100 => 010110 => 001011 => 2
[1,1,0,0,1,0] => 110010 => 011001 => 101100 => 2
[1,1,0,1,0,0] => 110100 => 011010 => 001101 => 2
[1,1,1,0,0,0] => 111000 => 011100 => 001110 => 3
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 10101010 => 1
[1,0,1,0,1,1,0,0] => 10101100 => 01010110 => 00101011 => 2
[1,0,1,1,0,0,1,0] => 10110010 => 01011001 => 10101100 => 2
[1,0,1,1,0,1,0,0] => 10110100 => 01011010 => 00101101 => 2
[1,0,1,1,1,0,0,0] => 10111000 => 01011100 => 00101110 => 3
[1,1,0,0,1,0,1,0] => 11001010 => 01100101 => 10110010 => 2
[1,1,0,0,1,1,0,0] => 11001100 => 01100110 => 00110011 => 2
[1,1,0,1,0,0,1,0] => 11010010 => 01101001 => 10110100 => 2
[1,1,0,1,0,1,0,0] => 11010100 => 01101010 => 00110101 => 2
[1,1,0,1,1,0,0,0] => 11011000 => 01101100 => 00110110 => 2
[1,1,1,0,0,0,1,0] => 11100010 => 01110001 => 10111000 => 3
[1,1,1,0,0,1,0,0] => 11100100 => 01110010 => 00111001 => 3
[1,1,1,0,1,0,0,0] => 11101000 => 01110100 => 00111010 => 3
[1,1,1,1,0,0,0,0] => 11110000 => 01111000 => 00111100 => 4
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0101010101 => 1010101010 => 1
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0101010110 => 0010101011 => 2
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0101011001 => 1010101100 => 2
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0101011010 => 0010101101 => 2
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0101011100 => 0010101110 => 3
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0101100101 => 1010110010 => 2
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0101100110 => 0010110011 => 2
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0101101001 => 1010110100 => 2
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0101101010 => 0010110101 => 2
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0101101100 => 0010110110 => 2
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0101110001 => 1010111000 => 3
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0101110100 => 0010111010 => 3
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0101111000 => 0010111100 => 4
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0110010101 => 1011001010 => 2
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0110010110 => 0011001011 => 2
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0110011001 => 1011001100 => 2
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0110011010 => 0011001101 => 2
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0110100101 => 1011010010 => 2
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0110100110 => 0011010011 => 2
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0110101001 => 1011010100 => 2
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 0110101010 => 0011010101 => 2
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0110110001 => 1011011000 => 3
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0111000101 => 1011100010 => 3
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0111001001 => 1011100100 => 3
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 0111001100 => 0011100110 => 3
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0111010001 => 1011101000 => 3
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 0111010100 => 0011101010 => 3
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 0111011000 => 0011101100 => 3
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0111100001 => 1011110000 => 4
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 0111100100 => 0011110010 => 4
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 0111101000 => 0011110100 => 4
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0111110000 => 0011111000 => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 010101010101 => 101010101010 => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 010101010110 => 001010101011 => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 010101011001 => 101010101100 => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 010101011010 => 001010101101 => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 010101100101 => 101010110010 => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 010101100110 => 001010110011 => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 010101101001 => 101010110100 => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 010101101010 => 001010110101 => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 010101110001 => 101010111000 => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 010110010101 => 101011001010 => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 010110010110 => 001011001011 => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 010110011001 => 101011001100 => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 010110011010 => 001011001101 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 010110100101 => 101011010010 => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 010110100110 => 001011010011 => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 010110101001 => 101011010100 => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 010110101010 => 001011010101 => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 010110101100 => 001011010110 => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 010110110001 => 101011011000 => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 010110110100 => 001011011010 => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 010110111000 => 001011011100 => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 010111000101 => 101011100010 => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 010111001001 => 101011100100 => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 010111001100 => 001011100110 => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 010111010001 => 101011101000 => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 010111010100 => 001011101010 => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 010111011000 => 001011101100 => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 010111100001 => 101011110000 => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 010111100100 => 001011110010 => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 010111101000 => 001011110100 => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 010111110000 => 001011111000 => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 011001010101 => 101100101010 => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 011001010110 => 001100101011 => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 011001011001 => 101100101100 => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 011001011010 => 001100101101 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 011001100101 => 101100110010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 011001100110 => 001100110011 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 011001101001 => 101100110100 => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 011001101010 => 001100110101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 011001110001 => 101100111000 => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 011010010101 => 101101001010 => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 011010010110 => 001101001011 => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 011010011001 => 101101001100 => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 011010011010 => 001101001101 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 011010100101 => 101101010010 => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 011010100110 => 001101010011 => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 011010101001 => 101101010100 => 2
>>> Load all 137 entries. <<<
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Description
The length of the longest constant subword.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
This is the word obtained by moving the last letter to the beginnig.
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