Identifier
- St000628: Binary words ⟶ ℤ
Values
=>
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111111100100000010=>6
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101111111001000000=>7
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11111111010000000010=>8
10111111110100000000=>8
1111111111000000000010=>10
1011111111110000000000=>10
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Description
The balance of a binary word.
The balance of a word is the smallest number $q$ such that the word is $q$-balanced [1].
A binary word $w$ is $q$-balanced if for any two factors $u$, $v$ of $w$ of the same length, the difference between the number of ones in $u$ and $v$ is at most $q$.
The balance of a word is the smallest number $q$ such that the word is $q$-balanced [1].
A binary word $w$ is $q$-balanced if for any two factors $u$, $v$ of $w$ of the same length, the difference between the number of ones in $u$ and $v$ is at most $q$.
References
[1] Vuillon, L. Balanced words MathSciNet:2073026 zbMATH:02174595
Code
def statistic(w): return w.balance()
Created
Oct 16, 2016 at 21:54 by Martin Rubey
Updated
Dec 28, 2017 at 14:20 by Martin Rubey
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