BALANCED WORDS AND MAJORIZATION
Oliver Jenkinson · Discrete Mathematics Algorithms and Applications · 2009
When expressed in terms of base-2 expanions, balanced words are majorized by other words of the same slope. Consequently they have smaller standard deviation and larger geometric mean than all words with given arithmetic mean (or slope), they can be expressed as a doubly stochastic average of any such word, and they can be derived from any such word by a finite number of transfers.