Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001372
Mapping
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
St001372: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 10 => 01 => 01 => 1
[1,0,1,0]
 => 1010 => 0101 => 1001 => 2
[1,1,0,0]
 => 1100 => 1001 => 0101 => 1
[1,0,1,0,1,0]
 => 101010 => 010101 => 110001 => 3
[1,0,1,1,0,0]
 => 101100 => 011001 => 010101 => 1
[1,1,0,0,1,0]
 => 110010 => 100101 => 101001 => 2
[1,1,0,1,0,0]
 => 110100 => 101001 => 011001 => 2
[1,1,1,0,0,0]
 => 111000 => 110001 => 001101 => 2
[1,0,1,0,1,0,1,0]
 => 10101010 => 01010101 => 11100001 => 4
[1,0,1,0,1,1,0,0]
 => 10101100 => 01011001 => 01100101 => 2
[1,0,1,1,0,0,1,0]
 => 10110010 => 01100101 => 10101001 => 2
[1,0,1,1,0,1,0,0]
 => 10110100 => 01101001 => 01101001 => 2
[1,0,1,1,1,0,0,0]
 => 10111000 => 01110001 => 00101101 => 2
[1,1,0,0,1,0,1,0]
 => 11001010 => 10010101 => 11010001 => 3
[1,1,0,0,1,1,0,0]
 => 11001100 => 10011001 => 01010101 => 1
[1,1,0,1,0,0,1,0]
 => 11010010 => 10100101 => 10110001 => 2
[1,1,0,1,0,1,0,0]
 => 11010100 => 10101001 => 01110001 => 3
[1,1,0,1,1,0,0,0]
 => 11011000 => 10110001 => 00110101 => 2
[1,1,1,0,0,0,1,0]
 => 11100010 => 11000101 => 10011001 => 2
[1,1,1,0,0,1,0,0]
 => 11100100 => 11001001 => 01011001 => 2
[1,1,1,0,1,0,0,0]
 => 11101000 => 11010001 => 00111001 => 3
[1,1,1,1,0,0,0,0]
 => 11110000 => 11100001 => 00011101 => 3
[1,0,1,0,1,0,1,0,1,0]
 => 1010101010 => 0101010101 => 1111000001 => 5
[1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => 0101011001 => 0111000101 => 3
[1,0,1,0,1,1,0,0,1,0]
 => 1010110010 => 0101100101 => 1011001001 => 2
[1,0,1,0,1,1,0,1,0,0]
 => 1010110100 => 0101101001 => 0111001001 => 3
[1,0,1,0,1,1,1,0,0,0]
 => 1010111000 => 0101110001 => 0011001101 => 2
[1,0,1,1,0,0,1,0,1,0]
 => 1011001010 => 0110010101 => 1101010001 => 3
[1,0,1,1,0,0,1,1,0,0]
 => 1011001100 => 0110011001 => 0101010101 => 1
[1,0,1,1,0,1,0,0,1,0]
 => 1011010010 => 0110100101 => 1011010001 => 2
[1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => 0110101001 => 0111010001 => 3
[1,0,1,1,0,1,1,0,0,0]
 => 1011011000 => 0110110001 => 0011010101 => 2
[1,0,1,1,1,0,0,0,1,0]
 => 1011100010 => 0111000101 => 1001011001 => 2
[1,0,1,1,1,0,0,1,0,0]
 => 1011100100 => 0111001001 => 0101011001 => 2
[1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => 0111100001 => 0001011101 => 3
[1,1,0,0,1,0,1,0,1,0]
 => 1100101010 => 1001010101 => 1110100001 => 4
[1,1,0,0,1,0,1,1,0,0]
 => 1100101100 => 1001011001 => 0110100101 => 2
[1,1,0,0,1,1,0,0,1,0]
 => 1100110010 => 1001100101 => 1010101001 => 2
[1,1,0,0,1,1,0,1,0,0]
 => 1100110100 => 1001101001 => 0110101001 => 2
[1,1,0,0,1,1,1,0,0,0]
 => 1100111000 => 1001110001 => 0010101101 => 2
[1,1,0,1,0,0,1,0,1,0]
 => 1101001010 => 1010010101 => 1101100001 => 3
[1,1,0,1,0,0,1,1,0,0]
 => 1101001100 => 1010011001 => 0101100101 => 2
[1,1,0,1,0,1,0,0,1,0]
 => 1101010010 => 1010100101 => 1011100001 => 3
[1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => 1010101001 => 0111100001 => 4
[1,1,0,1,1,0,0,0,1,0]
 => 1101100010 => 1011000101 => 1001101001 => 2
[1,1,0,1,1,0,0,1,0,0]
 => 1101100100 => 1011001001 => 0101101001 => 2
[1,1,0,1,1,1,0,0,0,0]
 => 1101110000 => 1011100001 => 0001101101 => 2
[1,1,1,0,0,0,1,0,1,0]
 => 1110001010 => 1100010101 => 1100110001 => 3
[1,1,1,0,0,0,1,1,0,0]
 => 1110001100 => 1100011001 => 0100110101 => 2
[1,1,1,0,0,1,0,0,1,0]
 => 1110010010 => 1100100101 => 1010110001 => 2
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.