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Identifier

St001267: Binary words ⟶ ℤ

Values

0 => 1

1 => 1

00 => 2

01 => 1

10 => 2

11 => 2

000 => 3

001 => 1

010 => 2

011 => 1

100 => 3

101 => 2

110 => 3

111 => 3

0000 => 4

0001 => 1

0010 => 2

0011 => 1

0100 => 3

0101 => 2

0110 => 2

0111 => 1

1000 => 4

1001 => 2

1010 => 3

1011 => 2

1100 => 4

1101 => 3

1110 => 4

1111 => 4

00000 => 5

00001 => 1

00010 => 2

00011 => 1

00100 => 3

00101 => 1

00110 => 2

00111 => 1

01000 => 4

01001 => 2

01010 => 3

01011 => 1

01100 => 3

01101 => 2

01110 => 2

01111 => 1

10000 => 5

10001 => 2

10010 => 3

10011 => 2

10100 => 4

10101 => 3

10110 => 3

10111 => 2

11000 => 5

11001 => 3

11010 => 4

11011 => 3

11100 => 5

11101 => 4

11110 => 5

11111 => 5

000000 => 6

000001 => 1

000010 => 2

000011 => 1

000100 => 3

000101 => 1

000110 => 2

000111 => 1

001000 => 4

001001 => 2

001010 => 2

001011 => 1

001100 => 3

001101 => 1

001110 => 2

001111 => 1

010000 => 5

010001 => 2

010010 => 3

010011 => 2

010100 => 4

010101 => 3

010110 => 2

010111 => 1

011000 => 4

011001 => 2

011010 => 3

011011 => 2

011100 => 3

011101 => 2

011110 => 2

011111 => 1

100000 => 6

100001 => 2

100010 => 3

100011 => 2

100100 => 4

100101 => 2

100110 => 3

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Description

The length of the Lyndon factorization of the binary word.
The Lyndon factorization of a finite word w is its unique factorization as a non-increasing product of Lyndon words, i.e., $w = l_1\dots l_n$ where each $l_i$ is a Lyndon word and $l_1 \geq\dots\geq l_n$.

References

[1] wikipedia:Lyndon word
[2] Duval, J.-P. Factorizing words over an ordered alphabet MathSciNet:0729232

Code

def statistic(w):
    return len(w.lyndon_factorization())

Created

Oct 05, 2018 at 09:42 by Martin Rubey

Updated

Oct 05, 2018 at 09:42 by Martin Rubey