Balanced word: Difference between revisions

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A [[word]] or [[necklace]] ''s'' is '''balanced''' if its '''block balance'''{{idiosyncratic}} satisfies the following:
A [[word]] or [[necklace]] ''s'' is '''balanced''' if its '''block balance'''{{idiosyncratic}} satisfies the following:


<math> \mathsf{block\_balance}(s) := \max_{a, k} \big\{ \big| |w|_{a} - |w'|_{a} \big| : a \text{ is a letter of }s\text{ and }w, w'\text{ are length-}k \text{ subwords of } s\big\} \leq 1,</math>
<math> \mathsf{block\_balance}(s) := \max \big\{ \big| |w|_{a} - |w'|_{a} \big| : a \text{ is a letter of }s\text{ and }w, w'\text{ are length-}k \text{ subwords of } s\big\} \leq 1,</math>


where |''u''|<sub>''a''</sub> is the number of occurrences of the letter ''a'' in the word ''u''.
where |''u''|<sub>''a''</sub> is the number of occurrences of the letter ''a'' in the word ''u''.