Balanced word: Difference between revisions

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Let ''d'' ≥ 0. A scale word ''s'' is ''d''-'''balanced''' if its '''balance''' satisfies the following:
Let ''d'' ≥ 0. A linear or circular word ''s'' is ''d''-'''balanced''' if its '''balance''' satisfies the following:


<math> \operatorname{balance}(s) := \max \big\{ \big| |w|_{x_i} - |w'|_{x_i} \big| : x_i \text{ is a letter of }s\text{ and }k = \operatorname{len}(w) = \operatorname{len}(w') \big\} \leq d,</math>
<math> \operatorname{balance}(s) := \max \big\{ \big| |w|_{x_i} - |w'|_{x_i} \big| : x_i \text{ is a letter of }s\text{ and }k = \operatorname{len}(w) = \operatorname{len}(w') \big\} \leq d,</math>