- FindStat

Identifier

Mp00261: Binary words —Burrows-Wheeler⟶ Binary words
St000983: Binary words ⟶ ℤ

Values

0 => 0 => 1

1 => 1 => 1

00 => 00 => 1

01 => 10 => 2

10 => 10 => 2

11 => 11 => 1

000 => 000 => 1

001 => 100 => 2

010 => 100 => 2

011 => 110 => 2

100 => 100 => 2

101 => 110 => 2

110 => 110 => 2

111 => 111 => 1

0000 => 0000 => 1

0001 => 1000 => 2

0010 => 1000 => 2

0011 => 1010 => 4

0100 => 1000 => 2

0101 => 1100 => 2

0110 => 1010 => 4

0111 => 1110 => 2

1000 => 1000 => 2

1001 => 1010 => 4

1010 => 1100 => 2

1011 => 1110 => 2

1100 => 1010 => 4

1101 => 1110 => 2

1110 => 1110 => 2

1111 => 1111 => 1

00000 => 00000 => 1

00001 => 10000 => 2

00010 => 10000 => 2

00011 => 10010 => 3

00100 => 10000 => 2

00101 => 11000 => 2

00110 => 10010 => 3

00111 => 10110 => 3

01000 => 10000 => 2

01001 => 11000 => 2

01010 => 11000 => 2

01011 => 11100 => 2

01100 => 10010 => 3

01101 => 11100 => 2

01110 => 10110 => 3

01111 => 11110 => 2

10000 => 10000 => 2

10001 => 10010 => 3

10010 => 11000 => 2

10011 => 10110 => 3

10100 => 11000 => 2

10101 => 11100 => 2

10110 => 11100 => 2

10111 => 11110 => 2

11000 => 10010 => 3

11001 => 10110 => 3

11010 => 11100 => 2

11011 => 11110 => 2

11100 => 10110 => 3

11101 => 11110 => 2

11110 => 11110 => 2

11111 => 11111 => 1

000000 => 000000 => 1

000001 => 100000 => 2

000010 => 100000 => 2

000011 => 100010 => 3

000100 => 100000 => 2

000101 => 101000 => 4

000110 => 100010 => 3

000111 => 100110 => 2

001000 => 100000 => 2

001001 => 110000 => 2

001010 => 101000 => 4

001011 => 101100 => 3

001100 => 100010 => 3

001101 => 110010 => 3

001110 => 100110 => 2

001111 => 101110 => 3

010000 => 100000 => 2

010001 => 101000 => 4

010010 => 110000 => 2

010011 => 110010 => 3

010100 => 101000 => 4

010101 => 111000 => 2

010110 => 101100 => 3

010111 => 111010 => 4

011000 => 100010 => 3

011001 => 101100 => 3

011010 => 110010 => 3

011011 => 111100 => 2

011100 => 100110 => 2

011101 => 111010 => 4

011110 => 101110 => 3

011111 => 111110 => 2

100000 => 100000 => 2

100001 => 100010 => 3

100010 => 101000 => 4

100011 => 100110 => 2

100100 => 110000 => 2

100101 => 101100 => 3

100110 => 110010 => 3

>>> Load all 1022 entries. <<<

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$F_{1} = 2\ q$

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

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

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

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

$F_{6} = 2\ q + 26\ q^{2} + 24\ q^{3} + 12\ q^{4}$

$F_{7} = 2\ q + 70\ q^{2} + 42\ q^{3} + 14\ q^{4}$

$F_{8} = 2\ q + 86\ q^{2} + 96\ q^{3} + 48\ q^{4} + 16\ q^{5} + 8\ q^{6}$

$F_{9} = 2\ q + 204\ q^{2} + 216\ q^{3} + 54\ q^{4} + 18\ q^{5} + 18\ q^{8}$

Description

The length of the longest alternating subword.
This is the length of the longest consecutive subword of the form

$010...$ or of the form

$101...$ .

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.