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== Theorem 9 (Ternary product words) == | |||
If a [[product word]] of two MOS words of the same length is ternary, then it is pairwise-MOS. | |||
=== Proof === | |||
Assume that the product of two MOS words ''v''('''a''', '''b''') and ''w''('''c''', '''d''') contains exactly three letters, say ('''a''', '''c'''), ('''a''', '''d'''), ('''b''', '''c'''). Equating ('''a''', '''c''') and ('''a''', '''d''') recovers ''v'', and equating ('''a''', '''c''') and ('''b''', '''c''') recovers ''w''. What does equating ('''a''', '''d''') and ('''b''', '''c''') do? | |||
Latest revision as of 03:24, 3 January 2026
Theorem 9 (Ternary product words)
If a product word of two MOS words of the same length is ternary, then it is pairwise-MOS.
Proof
Assume that the product of two MOS words v(a, b) and w(c, d) contains exactly three letters, say (a, c), (a, d), (b, c). Equating (a, c) and (a, d) recovers v, and equating (a, c) and (b, c) recovers w. What does equating (a, d) and (b, c) do?