Independent set counts for trees grow with exponent at least 0.1966; planar graphs achieve density one; graphs with linear edge density realize all positive integers via Zaremba's conjecture.
On some results of K orobov and L archer and Z aremba's conjecture
2 Pith papers cite this work. Polarity classification is still indexing.
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By proving expansion in SL₂(ℤ/qℤ) and applying Shkredov's framework, the paper confirms Zaremba's conjecture.
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Independent Sets and Continued Fractions
Independent set counts for trees grow with exponent at least 0.1966; planar graphs achieve density one; graphs with linear edge density realize all positive integers via Zaremba's conjecture.
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Expansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjecture
By proving expansion in SL₂(ℤ/qℤ) and applying Shkredov's framework, the paper confirms Zaremba's conjecture.