Generator-offset property: Difference between revisions
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== Open conjectures == | == Open conjectures == | ||
=== Conjecture 3 === | === Conjecture 3 ("MV3 Structure Theorem") === | ||
If a non-multiperiod 3-step size scale word is | If a non-multiperiod 3-step size scale word is | ||
# unconditionally MV3, | # unconditionally MV3, | ||
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# is not of the form ''mx my mz'', ''xyzyx'' or ''xyxzxyx'', | # is not of the form ''mx my mz'', ''xyzyx'' or ''xyxzxyx'', | ||
then it is SGA. (a converse to Theorem 1) | then it is SGA. (a converse to Theorem 1) | ||
If a non-multiperiod 3-step size scale word is | If a non-multiperiod 3-step size scale word is | ||
# unconditionally MV3, | # unconditionally MV3, | ||
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then it is of the form ''W''(''x'', ''y'', ''z'')''W''(''y'', ''x'', ''z'') for some word ''W'' in 3 variables. | then it is of the form ''W''(''x'', ''y'', ''z'')''W''(''y'', ''x'', ''z'') for some word ''W'' in 3 variables. | ||
=== Conjecture | === Conjecture 4 === | ||
An SGA scale is always pairwise-well-formed. That is, the result of identifying any two step sizes of an SGA scale is always a non-multiperiod mos. | An SGA scale is always pairwise-well-formed. That is, the result of identifying any two step sizes of an SGA scale is always a non-multiperiod mos. | ||