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On the Ordering and Injectivity of Lagrange Constants Associated with Certain Substitutions
Motivated by the modern characterization of the Markoff spectrum via mechanical words and the Markoff Uniqueness Conjecture, we study the Lagrange constants of continued fractions generated by a parameterized family of substitutions $ϕ_{a,b}$ $ϕ_{a,b}$ defined by $0 \mapsto aa$ and $1 \mapsto bb$
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