Theorems · Theorem · combinatorics
Nat.multinomial_spec
∀ {α : Type u_1} (s : Finset α) (f : α → ℕ), (∏ i ∈ s, (f i).factorial) * Nat.multinomial s f = (∑ i ∈ s, f i).factorial- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement · cited by 5,195
- Finset.prodstatement · cited by 2,356
- Nat.factorialstatement · cited by 616
- Nat.multinomialstatement · cited by 34
- Nat.prod_factorial_dvd_factorial_sumproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Multiset.bell_mul_eqproof · cited by 2
- Nat.multinomial_congr_of_eq_on_interproof · cited by 1
- Nat.binomial_specproof · cited by 0
- Nat.multinomial_singleproof · cited by 0