Balanced word: Difference between revisions
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Let ''a'' be a letter in a [[word]] or [[necklace]] ''s''. Define | Let ''a'' be a letter in a [[word]] or [[necklace]] ''s''. Define | ||
<math> \mathsf{block\_balance}(s, a) := \max \big\{ \big| |w|_{a} - |w'|_{a} \big| : w | <math> \mathsf{block\_balance}(s, a) := \max \big\{ \big| |w|_{a} - |w'|_{a} \big| : |w| = |w'| \big\},</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'' and |''u''| is the length of the word ''u''. | ||
Then ''s'' is '''balanced''' if its '''block balance'''{{idiosyncratic}} satisfies the following: | Then ''s'' is '''balanced''' if its '''block balance'''{{idiosyncratic}} satisfies the following: | ||