Ternary scale theorems: Difference between revisions
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## Interchange some of the Z's and X's at some (possibly none) of the borders of these copies of the mos word ''w''. | ## Interchange some of the Z's and X's at some (possibly none) of the borders of these copies of the mos word ''w''. | ||
## Replace every other X with Y in ''w''. | ## Replace every other X with Y in ''w''. | ||
# Single-period MV3 scales not of type (3), or of type (3) with no twisting, are always SV3. | # Single-period MV3 scales not of type (3), or of type (3) with no twisting at step 2, are always SV3. | ||
=== Proof === | === Proof === | ||
Proven by Bulgakova, Buzhinsky and Goncharov (2023), "[https://www.sciencedirect.com/science/article/pii/S0304397522006417 On balanced and abelian properties of circular words over a ternary alphabet]" (and Theorem 4). | Proven by Bulgakova, Buzhinsky and Goncharov (2023), "[https://www.sciencedirect.com/science/article/pii/S0304397522006417 On balanced and abelian properties of circular words over a ternary alphabet]" (and Theorem 4). | ||