- FindStat

Identifier

Mp00261: Binary words —Burrows-Wheeler⟶ Binary words
St000691: Binary words ⟶ ℤ

Values

0 => 0 => 0

1 => 1 => 0

00 => 00 => 0

01 => 10 => 1

10 => 10 => 1

11 => 11 => 0

000 => 000 => 0

001 => 100 => 1

010 => 100 => 1

011 => 110 => 1

100 => 100 => 1

101 => 110 => 1

110 => 110 => 1

111 => 111 => 0

0000 => 0000 => 0

0001 => 1000 => 1

0010 => 1000 => 1

0011 => 1010 => 3

0100 => 1000 => 1

0101 => 1100 => 1

0110 => 1010 => 3

0111 => 1110 => 1

1000 => 1000 => 1

1001 => 1010 => 3

1010 => 1100 => 1

1011 => 1110 => 1

1100 => 1010 => 3

1101 => 1110 => 1

1110 => 1110 => 1

1111 => 1111 => 0

00000 => 00000 => 0

00001 => 10000 => 1

00010 => 10000 => 1

00011 => 10010 => 3

00100 => 10000 => 1

00101 => 11000 => 1

00110 => 10010 => 3

00111 => 10110 => 3

01000 => 10000 => 1

01001 => 11000 => 1

01010 => 11000 => 1

01011 => 11100 => 1

01100 => 10010 => 3

01101 => 11100 => 1

01110 => 10110 => 3

01111 => 11110 => 1

10000 => 10000 => 1

10001 => 10010 => 3

10010 => 11000 => 1

10011 => 10110 => 3

10100 => 11000 => 1

10101 => 11100 => 1

10110 => 11100 => 1

10111 => 11110 => 1

11000 => 10010 => 3

11001 => 10110 => 3

11010 => 11100 => 1

11011 => 11110 => 1

11100 => 10110 => 3

11101 => 11110 => 1

11110 => 11110 => 1

11111 => 11111 => 0

000000 => 000000 => 0

000001 => 100000 => 1

000010 => 100000 => 1

000011 => 100010 => 3

000100 => 100000 => 1

000101 => 101000 => 3

000110 => 100010 => 3

000111 => 100110 => 3

001000 => 100000 => 1

001001 => 110000 => 1

001010 => 101000 => 3

001011 => 101100 => 3

001100 => 100010 => 3

001101 => 110010 => 3

001110 => 100110 => 3

001111 => 101110 => 3

010000 => 100000 => 1

010001 => 101000 => 3

010010 => 110000 => 1

010011 => 110010 => 3

010100 => 101000 => 3

010101 => 111000 => 1

010110 => 101100 => 3

010111 => 111010 => 3

011000 => 100010 => 3

011001 => 101100 => 3

011010 => 110010 => 3

011011 => 111100 => 1

011100 => 100110 => 3

011101 => 111010 => 3

011110 => 101110 => 3

011111 => 111110 => 1

100000 => 100000 => 1

100001 => 100010 => 3

100010 => 101000 => 3

100011 => 100110 => 3

100100 => 110000 => 1

100101 => 101100 => 3

100110 => 110010 => 3

>>> Load all 1022 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

$F_{1} = 2$

$F_{2} = 2 + 2\ q$

$F_{3} = 2 + 6\ q$

$F_{4} = 2 + 10\ q + 4\ q^{3}$

$F_{5} = 2 + 20\ q + 10\ q^{3}$

$F_{6} = 2 + 20\ q + 42\ q^{3}$

$F_{7} = 2 + 42\ q + 70\ q^{3} + 14\ q^{5}$

$F_{8} = 2 + 42\ q + 140\ q^{3} + 72\ q^{5}$

$F_{9} = 2 + 60\ q + 288\ q^{3} + 126\ q^{5} + 36\ q^{7}$

Description

The number of changes of a binary word.
This is the number of indices

$i$ such that

$w_i \neq w_{i+1}$ .

Map

Burrows-Wheeler

Description

The Burrows-Wheeler transform of a binary word.
The Burrows-Wheeler transform of a finite word

$w$ is obtained from

$w$ by first listing the conjugates of

$w$ in lexicographic order and then concatenating the final letters of the conjugates in this order.