User:Inthar/MV3: Difference between revisions

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=== MV3 Theorem 1 ===
=== MV3 Theorem 1 ===
''The following are equivalent for a scale word S with steps x, y, z:''
''The following are equivalent for a non-multiperiod scale word S with steps x, y, z:''
# ''S is MV3.''
# ''S is MV3.''
# ''S is PMOS, or S is of the form x'y'z'y'x' or its repetitions.''
# ''S is PMOS, or S is of the form x'y'z'y'x' or its repetitions.''
# ''S is AG, or S is of the form x'y'z'y'x' or its repetitions, or x'y'x'z'x'y'x' or its repetitions.''
# ''S is AG, or S is of the form x'y'z'y'x' or its repetitions, or x'y'x'z'x'y'x' or its repetitions.''
Below, assume that the scale word S is not multiperiod.


==== Lemma 1: S is pairwise MOS (PMOS) except in the case "xyzyx" ====
==== Lemma 1: S is pairwise MOS (PMOS) except in the case "xyzyx" ====