Non-degenerate Bedford-McMullen carpets have no oblique self-embedding similitudes, implying logarithmic commensurability of ratios, with a new proof, an oblique-symmetric generalized Sierpiński carpet construction, and a tan(±1) restriction on rotational angles under strong separation.
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Self-embedding similitudes of Bedford-McMullen carpets with dependent ratios
Non-degenerate Bedford-McMullen carpets have no oblique self-embedding similitudes, implying logarithmic commensurability of ratios, with a new proof, an oblique-symmetric generalized Sierpiński carpet construction, and a tan(±1) restriction on rotational angles under strong separation.