Ternary parallelogram scales are MOS substitution: Difference between revisions
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as φ is a homomorphism. Hence corresponding elements of any two ''m'' × ''n'' windows get the same {{nowrap|ℤ/''mn''ℤ}} labeling under φ modulo a shift. | as φ is a homomorphism. Hence corresponding elements of any two ''m'' × ''n'' windows get the same {{nowrap|ℤ/''mn''ℤ}} labeling under φ modulo a shift. | ||
=== Step 3: By ternarity, | === Step 3: By ternarity, one of the 1-step vectors is parallel to a coordinate axis === | ||
Consider the following four "quadrants": | Consider the following four "quadrants": | ||
# ''Q''<sub>1</sub> = [0 : ''m''] × [0 : ''n''] | # ''Q''<sub>1</sub> = [0 : ''m''] × [0 : ''n''] | ||