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.
On q-deformed Markov numbers
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Multiple equivalent combinatorial expansion formulas are given for generalized cluster algebras from arcs on punctured orbifolds, generalizing prior surface and orbifold cases.
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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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Cluster Expansions from Punctured Orbifolds
Multiple equivalent combinatorial expansion formulas are given for generalized cluster algebras from arcs on punctured orbifolds, generalizing prior surface and orbifold cases.
- Wug-snake graphs and Markov numbers of matrix semigroups