Generator-offset property: Difference between revisions
→Open questions: should have at least 3 notes |
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== Open conjectures == | == Open conjectures == | ||
=== Conjecture (" | === Conjecture ("SV3 Structure Theorem") === | ||
==== Conjecture 1 ==== | ==== Conjecture 1 ==== | ||
If a 3-step size scale word ''ax by cz'' is | If a 3-step size scale word ''ax by cz'' is | ||
# unconditionally | # unconditionally SV3 (strict variety 3, i.e. every k-step except multiples of the equave comes in ''exactly'' 3 sizes), | ||
# has ''odd'' cardinality, | # has ''odd'' cardinality, | ||
# has gcd(''a'', ''b'', ''c'') = 1, | # has gcd(''a'', ''b'', ''c'') = 1, | ||
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==== Conjecture 2 ==== | ==== Conjecture 2 ==== | ||
If a | If a 3-step size scale word is | ||
# unconditionally | # unconditionally SV3 (strict variety 3, i.e. every k-step except multiples of the equave comes in ''exactly'' 3 sizes) | ||
# has ''even'' cardinality, and | # has ''even'' cardinality, and | ||
# is not of the form ''mx my mz'', | # is not of the form ''mx my mz'', | ||