- FindStat

Identifier

St001355: Binary words ⟶ ℤ

Values

0 => 0

1 => 0

00 => 0

01 => 1

10 => 1

11 => 0

000 => 0

001 => 0

010 => 1

011 => 1

100 => 1

101 => 1

110 => 0

111 => 0

0000 => 0

0001 => 0

0010 => 0

0011 => 1

0100 => 1

0101 => 2

0110 => 2

0111 => 1

1000 => 1

1001 => 2

1010 => 2

1011 => 1

1100 => 1

1101 => 0

1110 => 0

1111 => 0

00000 => 0

00001 => 0

00010 => 0

00011 => 0

00100 => 0

00101 => 0

00110 => 1

00111 => 1

01000 => 1

01001 => 1

01010 => 2

01011 => 2

01100 => 2

01101 => 2

01110 => 1

01111 => 1

10000 => 1

10001 => 1

10010 => 2

10011 => 2

10100 => 2

10101 => 2

10110 => 1

10111 => 1

11000 => 1

11001 => 1

11010 => 0

11011 => 0

11100 => 0

11101 => 0

11110 => 0

11111 => 0

000000 => 0

000001 => 0

000010 => 0

000011 => 0

000100 => 0

000101 => 0

000110 => 0

000111 => 1

001000 => 0

001001 => 0

001010 => 0

001011 => 1

001100 => 1

001101 => 2

001110 => 2

001111 => 1

010000 => 1

010001 => 1

010010 => 1

010011 => 2

010100 => 2

010101 => 3

010110 => 3

010111 => 2

011000 => 2

011001 => 3

011010 => 3

011011 => 2

011100 => 2

011101 => 1

011110 => 1

011111 => 1

100000 => 1

100001 => 1

100010 => 1

100011 => 2

100100 => 2

100101 => 3

100110 => 3

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Description

Number of non-empty prefixes of a binary word that contain equally many 0's and 1's.
Graphically, this is the number of returns to the main diagonal of the monotone lattice path of a binary word.

Code

def statistic(P):
    return sum(1 for i in range(2,len(P)+1,2) if P[:i].count(0) == P[:i].count(1) )

Created

Feb 11, 2019 at 18:21 by Christian Stump

Updated

Feb 12, 2019 at 07:43 by Christian Stump