- FindStat

Identifier

Mp00224: Binary words —runsort⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
St000982: Binary words ⟶ ℤ

Values

0 => 0 => 0 => 1

1 => 1 => 1 => 1

00 => 00 => 01 => 1

01 => 01 => 10 => 1

10 => 01 => 10 => 1

11 => 11 => 11 => 2

000 => 000 => 011 => 2

001 => 001 => 101 => 1

010 => 001 => 101 => 1

011 => 011 => 110 => 2

100 => 001 => 101 => 1

101 => 011 => 110 => 2

110 => 011 => 110 => 2

111 => 111 => 111 => 3

0000 => 0000 => 0111 => 3

0001 => 0001 => 1011 => 2

0010 => 0001 => 1011 => 2

0011 => 0011 => 1101 => 2

0100 => 0001 => 1011 => 2

0101 => 0101 => 1000 => 3

0110 => 0011 => 1101 => 2

0111 => 0111 => 1110 => 3

1000 => 0001 => 1011 => 2

1001 => 0011 => 1101 => 2

1010 => 0011 => 1101 => 2

1011 => 0111 => 1110 => 3

1100 => 0011 => 1101 => 2

1101 => 0111 => 1110 => 3

1110 => 0111 => 1110 => 3

1111 => 1111 => 1111 => 4

00000 => 00000 => 01111 => 4

00001 => 00001 => 10111 => 3

00010 => 00001 => 10111 => 3

00011 => 00011 => 11011 => 2

00100 => 00001 => 10111 => 3

00101 => 00101 => 10001 => 3

00110 => 00011 => 11011 => 2

00111 => 00111 => 11101 => 3

01000 => 00001 => 10111 => 3

01001 => 00101 => 10001 => 3

01010 => 00101 => 10001 => 3

01011 => 01011 => 11000 => 3

01100 => 00011 => 11011 => 2

01101 => 01011 => 11000 => 3

01110 => 00111 => 11101 => 3

01111 => 01111 => 11110 => 4

10000 => 00001 => 10111 => 3

10001 => 00011 => 11011 => 2

10010 => 00011 => 11011 => 2

10011 => 00111 => 11101 => 3

10100 => 00011 => 11011 => 2

10101 => 01011 => 11000 => 3

10110 => 00111 => 11101 => 3

10111 => 01111 => 11110 => 4

11000 => 00011 => 11011 => 2

11001 => 00111 => 11101 => 3

11010 => 00111 => 11101 => 3

11011 => 01111 => 11110 => 4

11100 => 00111 => 11101 => 3

11101 => 01111 => 11110 => 4

11110 => 01111 => 11110 => 4

11111 => 11111 => 11111 => 5

000000 => 000000 => 011111 => 5

000001 => 000001 => 101111 => 4

000010 => 000001 => 101111 => 4

000011 => 000011 => 110111 => 3

000100 => 000001 => 101111 => 4

000101 => 000101 => 100011 => 3

000110 => 000011 => 110111 => 3

000111 => 000111 => 111011 => 3

001000 => 000001 => 101111 => 4

001001 => 001001 => 101001 => 2

001010 => 000101 => 100011 => 3

001011 => 001011 => 110001 => 3

001100 => 000011 => 110111 => 3

001101 => 001101 => 100101 => 2

001110 => 000111 => 111011 => 3

001111 => 001111 => 111101 => 4

010000 => 000001 => 101111 => 4

010001 => 000101 => 100011 => 3

010010 => 000101 => 100011 => 3

010011 => 001101 => 100101 => 2

010100 => 000101 => 100011 => 3

010101 => 010101 => 100000 => 5

010110 => 001011 => 110001 => 3

010111 => 010111 => 111000 => 3

011000 => 000011 => 110111 => 3

011001 => 001011 => 110001 => 3

011010 => 001011 => 110001 => 3

011011 => 011011 => 110010 => 2

011100 => 000111 => 111011 => 3

011101 => 010111 => 111000 => 3

011110 => 001111 => 111101 => 4

011111 => 011111 => 111110 => 5

100000 => 000001 => 101111 => 4

100001 => 000011 => 110111 => 3

100010 => 000011 => 110111 => 3

100011 => 000111 => 111011 => 3

100100 => 000011 => 110111 => 3

100101 => 001011 => 110001 => 3

100110 => 000111 => 111011 => 3

>>> Load all 1060 entries. <<<

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

runsort

Description

The word obtained by sorting the weakly increasing runs lexicographically.

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 $0\dots 0$.