Theorems · Theorem · combinatorics
SimpleGraph.isEquivalent_extremalNumber
∀ {W : Type u_1} {H : SimpleGraph W},
H.turanDensity ≠ 0 →
Asymptotics.IsEquivalent Filter.atTop (fun n => ↑(SimpleGraph.extremalNumber n H)) fun n =>
H.turanDensity * ↑(n.choose 2)extremalNumber n H is asymptotically equivalent to turanDensity H * n.choose 2 as n
approaches ∞.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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- SimpleGraphstatement and proof · cited by 3,072
- one_mulproof · cited by 2,841
- Filter.atTopstatement and proof · cited by 2,405
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- Filter.eventually_atTopproof · cited by 112
- Asymptotics.IsEquivalentstatement · cited by 98
- Filter.Tendsto.const_mulproof · cited by 55
- div_mul_div_commproof · cited by 24
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