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 \big\{ \big| |w|_{ | <math> \mathsf{block\_balance}(s) := \max \big\{ \big| |w|_{a} - |w'|_{a} \big| : a \text{ is a letter of }s\text{ and }k = \operatorname{len}(w) = \operatorname{len}(w') \big\} \leq 1,</math> | ||
where |''u''|<sub>''x''<sub>''i''</sub></sub> is the number of occurrences of the letter ''x''<sub>''i''</sub> in the word ''u''. | where |''u''|<sub>''x''<sub>''i''</sub></sub> is the number of occurrences of the letter ''x''<sub>''i''</sub> in the word ''u''. | ||