Balanced word: Difference between revisions

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 == Properties ==
 * A balanced word or necklace in ''N'' letters has a [[maximum variety]] bound of <math> N \choose {\lceil N/2 \rceil}</math>.
-* If ''w'' is an aperiodic infinite balanced word, then ''w'' is constructed via a finite sequence of ''congruence substitutions'' from infinite balanced words on 2 letters. A congruence substitution involves replacing the ''k''th letter of ''w'' with the ''k''th letter of ''a'' where ''a'' has a set of letters disjoint from that of ''w'' for all positive integers ''k''.<ref>Brauner, N., Crama, Y., Delaporte, E., Jost, V., & Libralesso, L. (2019). Do balanced words have a short period?. Theoretical Computer Science, 793, 169-180.</ref>
+* If ''w'' is an aperiodic infinite balanced word, then ''w'' is constructed via a finite sequence of ''congruence substitutions'' from infinite balanced words on 2 letters. A congruence substitution involves replacing the ''k''th occurrence of a fixed letter ''j'' in ''w'' with the ''k''th letter of ''a'' where ''a'' has a set of letters disjoint from that of ''w'' for all positive integers ''k''.<ref>Brauner, N., Crama, Y., Delaporte, E., Jost, V., & Libralesso, L. (2019). Do balanced words have a short period?. Theoretical Computer Science, 793, 169-180.</ref>
 == Generalizations ==