q-rationals are realized as circles in the plane with Springborn operations defined geometrically as homothety centers, producing a q-deformed midpoint formula and a new q-version of Markov numbers.
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q-metallic numbers have Taylor coefficient sequences characterized by recurrences or differential equations, with closed forms for n=1,2,3, asymptotics, modular identities, and a signed connection to RNA secondary structures.
citing papers explorer
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Plane geometry of $q$-rationals and Springborn Operations
q-rationals are realized as circles in the plane with Springborn operations defined geometrically as homothety centers, producing a q-deformed midpoint formula and a new q-version of Markov numbers.
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Analytical properties of $q$-metallic numbers
q-metallic numbers have Taylor coefficient sequences characterized by recurrences or differential equations, with closed forms for n=1,2,3, asymptotics, modular identities, and a signed connection to RNA secondary structures.