Identifier
-
Mp00093:
Dyck paths
—to binary word⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
St001372: Binary words ⟶ ℤ
Values
[1,0] => 10 => 01 => 10 => 1
[1,0,1,0] => 1010 => 0101 => 1010 => 1
[1,1,0,0] => 1100 => 0011 => 1001 => 2
[1,0,1,0,1,0] => 101010 => 010101 => 101010 => 1
[1,0,1,1,0,0] => 101100 => 001101 => 100110 => 2
[1,1,0,0,1,0] => 110010 => 010011 => 101001 => 2
[1,1,0,1,0,0] => 110100 => 001011 => 100101 => 2
[1,1,1,0,0,0] => 111000 => 000111 => 100011 => 3
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 10101010 => 1
[1,0,1,0,1,1,0,0] => 10101100 => 00110101 => 10011010 => 2
[1,0,1,1,0,0,1,0] => 10110010 => 01001101 => 10100110 => 2
[1,0,1,1,0,1,0,0] => 10110100 => 00101101 => 10010110 => 2
[1,0,1,1,1,0,0,0] => 10111000 => 00011101 => 10001110 => 3
[1,1,0,0,1,0,1,0] => 11001010 => 01010011 => 10101001 => 2
[1,1,0,0,1,1,0,0] => 11001100 => 00110011 => 10011001 => 2
[1,1,0,1,0,0,1,0] => 11010010 => 01001011 => 10100101 => 2
[1,1,0,1,0,1,0,0] => 11010100 => 00101011 => 10010101 => 2
[1,1,0,1,1,0,0,0] => 11011000 => 00011011 => 10001101 => 2
[1,1,1,0,0,0,1,0] => 11100010 => 01000111 => 10100011 => 3
[1,1,1,0,0,1,0,0] => 11100100 => 00100111 => 10010011 => 3
[1,1,1,0,1,0,0,0] => 11101000 => 00010111 => 10001011 => 3
[1,1,1,1,0,0,0,0] => 11110000 => 00001111 => 10000111 => 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 => 0011010101 => 1001101010 => 2
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0100110101 => 1010011010 => 2
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0010110101 => 1001011010 => 2
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0001110101 => 1000111010 => 3
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0101001101 => 1010100110 => 2
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0011001101 => 1001100110 => 2
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0100101101 => 1010010110 => 2
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0010101101 => 1001010110 => 2
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0001101101 => 1000110110 => 2
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0100011101 => 1010001110 => 3
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0010011101 => 1001001110 => 3
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0001011101 => 1000101110 => 3
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0000111101 => 1000011110 => 4
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0101010011 => 1010101001 => 2
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0011010011 => 1001101001 => 2
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0100110011 => 1010011001 => 2
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0010110011 => 1001011001 => 2
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0101001011 => 1010100101 => 2
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0011001011 => 1001100101 => 2
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0100101011 => 1010010101 => 2
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 0010101011 => 1001010101 => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 010101010101 => 101010101010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 010101010011 => 101010101001 => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 001101010011 => 100110101001 => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 010011010011 => 101001101001 => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 001011010011 => 100101101001 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 010100110011 => 101010011001 => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 001100110011 => 100110011001 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 010010110011 => 101001011001 => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 001010110011 => 100101011001 => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 010101001011 => 101010100101 => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 001101001011 => 100110100101 => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 010011001011 => 101001100101 => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 001011001011 => 100101100101 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 010100101011 => 101010010101 => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 001100101011 => 100110010101 => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 010010101011 => 101001010101 => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 001010101011 => 100101010101 => 2
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Description
The length of a longest cyclic run of ones of a binary word.
Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.
Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.
Map
reverse
Description
Return the reversal of a binary word.
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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