- FindStat

Identifier

Mp00105: Binary words —complement⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
St000392: Binary words ⟶ ℤ

Values

0 => 1 => 1 => 1

1 => 0 => 0 => 0

00 => 11 => 11 => 2

01 => 10 => 00 => 0

10 => 01 => 10 => 1

11 => 00 => 01 => 1

000 => 111 => 111 => 3

001 => 110 => 001 => 1

010 => 101 => 100 => 1

011 => 100 => 010 => 1

100 => 011 => 110 => 2

101 => 010 => 000 => 0

110 => 001 => 101 => 1

111 => 000 => 011 => 2

0000 => 1111 => 1111 => 4

0001 => 1110 => 0011 => 2

0010 => 1101 => 1001 => 1

0011 => 1100 => 0101 => 1

0100 => 1011 => 1100 => 2

0101 => 1010 => 0000 => 0

0110 => 1001 => 1010 => 1

0111 => 1000 => 0110 => 2

1000 => 0111 => 1110 => 3

1001 => 0110 => 0010 => 1

1010 => 0101 => 1000 => 1

1011 => 0100 => 0100 => 1

1100 => 0011 => 1101 => 2

1101 => 0010 => 0001 => 1

1110 => 0001 => 1011 => 2

1111 => 0000 => 0111 => 3

00000 => 11111 => 11111 => 5

00001 => 11110 => 00111 => 3

00010 => 11101 => 10011 => 2

00011 => 11100 => 01011 => 2

00100 => 11011 => 11001 => 2

00101 => 11010 => 00001 => 1

00110 => 11001 => 10101 => 1

00111 => 11000 => 01101 => 2

01000 => 10111 => 11100 => 3

01001 => 10110 => 00100 => 1

01010 => 10101 => 10000 => 1

01011 => 10100 => 01000 => 1

01100 => 10011 => 11010 => 2

01101 => 10010 => 00010 => 1

01110 => 10001 => 10110 => 2

01111 => 10000 => 01110 => 3

10000 => 01111 => 11110 => 4

10001 => 01110 => 00110 => 2

10010 => 01101 => 10010 => 1

10011 => 01100 => 01010 => 1

10100 => 01011 => 11000 => 2

10101 => 01010 => 00000 => 0

10110 => 01001 => 10100 => 1

10111 => 01000 => 01100 => 2

11000 => 00111 => 11101 => 3

11001 => 00110 => 00101 => 1

11010 => 00101 => 10001 => 1

11011 => 00100 => 01001 => 1

11100 => 00011 => 11011 => 2

11101 => 00010 => 00011 => 2

11110 => 00001 => 10111 => 3

11111 => 00000 => 01111 => 4

000000 => 111111 => 111111 => 6

000001 => 111110 => 001111 => 4

000010 => 111101 => 100111 => 3

000011 => 111100 => 010111 => 3

000100 => 111011 => 110011 => 2

000101 => 111010 => 000011 => 2

000110 => 111001 => 101011 => 2

000111 => 111000 => 011011 => 2

001000 => 110111 => 111001 => 3

001001 => 110110 => 001001 => 1

001010 => 110101 => 100001 => 1

001011 => 110100 => 010001 => 1

001100 => 110011 => 110101 => 2

001101 => 110010 => 000101 => 1

001110 => 110001 => 101101 => 2

001111 => 110000 => 011101 => 3

010000 => 101111 => 111100 => 4

010001 => 101110 => 001100 => 2

010010 => 101101 => 100100 => 1

010011 => 101100 => 010100 => 1

010100 => 101011 => 110000 => 2

010101 => 101010 => 000000 => 0

010110 => 101001 => 101000 => 1

010111 => 101000 => 011000 => 2

011000 => 100111 => 111010 => 3

011001 => 100110 => 001010 => 1

011010 => 100101 => 100010 => 1

011011 => 100100 => 010010 => 1

011100 => 100011 => 110110 => 2

011101 => 100010 => 000110 => 2

011110 => 100001 => 101110 => 3

011111 => 100000 => 011110 => 4

100000 => 011111 => 111110 => 5

100001 => 011110 => 001110 => 3

100010 => 011101 => 100110 => 2

100011 => 011100 => 010110 => 2

100100 => 011011 => 110010 => 2

100101 => 011010 => 000010 => 1

100110 => 011001 => 101010 => 1

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Description

The length of the longest run of ones in a binary word.

Map

complement

Description

Send a binary word to the word obtained by interchanging the two letters.

Map

flag zeros to zeros

Description

Return a binary word of the same length, such that the number of zeros equals the number of occurrences of $10$ in the word obtained from the original word by prepending the reverse of the complement.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.