Ternary scale theorems: Difference between revisions
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=== Theorem 6.1 (Classification of ternary balanced scales) === | === Theorem 6.1 (Classification of ternary balanced scales) === | ||
# A primitive [[balanced]] MV3 scale ''S'' is one of the following: | # A primitive [[balanced]] MV3 scale ''S'' is one of the following: | ||
## ''S'' is equivalent to '''XYXZXYX''. | ## ''S'' is equivalent to '''XYXZXYX'''. | ||
## len(''S'') is odd, and ''S'' is equivalent to a word constructed from taking the brightest mode of the MOS ''a'''''X''' ''b'''''Z''' with ''a'' even and gcd(''a'', ''b'') = 1, and replacing every other '''X''' with '''Y'''. We assume '''X''' > '''Z''' when constructing the MOS. | ## len(''S'') is odd, and ''S'' is equivalent to a word constructed from taking the brightest mode of the MOS ''a'''''X''' ''b'''''Z''' with ''a'' even and gcd(''a'', ''b'') = 1, and replacing every other '''X''' with '''Y'''. We assume '''X''' > '''Z''' when constructing the MOS. | ||
## If len(S) is even, then ''S'' is equivalent to a word constructed from taking the brightest mode of the MOS 2''a'''''X''' 2''b'''''Z''' with ''a'' odd and gcd(''a'', ''b'') = 1, and replacing every other '''X''' with '''Y'''. | ## If len(S) is even, then ''S'' is equivalent to a word constructed from taking the brightest mode of the MOS 2''a'''''X''' 2''b'''''Z''' with ''a'' odd and gcd(''a'', ''b'') = 1, and replacing every other '''X''' with '''Y'''. | ||