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.
Kogiso.q-deformations andt-deformations of Markov triples
2 Pith papers cite this work. Polarity classification is still indexing.
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For general triangulations, numerator and denominator polynomials of q-deformed continued fractions match q-frieze entries exactly and q-Farey polynomials up to explicit q-powers counted by the number of diagonals.
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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Degree shifts between q-deformed friezes and q-Farey labelings for general triangulations
For general triangulations, numerator and denominator polynomials of q-deformed continued fractions match q-frieze entries exactly and q-Farey polynomials up to explicit q-powers counted by the number of diagonals.