Generator-offset property: Difference between revisions

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 ## Replace every other X with Y in ''w''. The PWF scales are exactly the single-period rank-3 [[billiard scale]]s.
 # Non-twisted single-period MV3 scales are always SV3.
-# If the scale is PWF, with one exception abacaba, there always exists some "generator" interval such that the scale can be expressed as '''two parallel chains''' of this generator which are almost equal in length (the lengths are either equal, or differ by 1). This property is called the [[generator-offset property]] (GO).
 ==== Proof ====
 Proven in Bulgakova, Buzhinsky and Goncharov (2023), "On balanced and abelian properties of circular words over a ternary alphabet". Note that billiard scales are called "balanced words" in this paper.