Theorems · Theorem · combinatorics
isTheta_choose
∀ (k : ℕ), (fun n => ↑(n.choose k)) =Θ[Filter.atTop] fun n => ↑n ^ k
n.choose k is big-theta n^k.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Choose
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filter.atTopstatement and proof · cited by 2,405
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- div_eq_mul_invproof · cited by 715
- Nat.factorialproof · cited by 616
- Nat.choosestatement · cited by 494
- Asymptotics.IsThetastatement and proof · cited by 115
- inv_ne_zeroproof · cited by 99
- CommMagmaproof · cited by 57
- Nat.factorial_ne_zeroproof · cited by 56
- Asymptotics.IsTheta.const_mul_leftproof · cited by 8
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.