User:Inthar/Sandbox

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?