Theorems · Theorem · combinatorics
Multiset.multinomial_nsmul
∀ (k : ℕ) (m : Multiset ℕ), (k • m).multinomial = (Nat.multinomial (Finset.range k) fun x => m.sum) * m.multinomial ^ k
- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Multisetstatement and proof · cited by 2,627
- Finset.rangestatement and proof · cited by 1,341
- pow_zeroproof · cited by 1,094
- Nat.chooseproof · cited by 494
- Multiset.sumstatement and proof · cited by 388
- Finset.sum_constproof · cited by 254
- pow_succ'proof · cited by 228
- zero_nsmulproof · cited by 137
- Finset.card_rangeproof · cited by 108
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.multinomial_nsmul_singletonproof · cited by 1