Theorems · Theorem · combinatorics
Sym.card_sym_eq_choose
∀ {α : Type u_2} [inst : Fintype α] (k : ℕ) [inst_1 : Fintype (Sym α k)],
Fintype.card (Sym α k) = (Fintype.card α + k - 1).choose kThe stars and bars lemma: the cardinality of Sym α k is equal to
Nat.choose (card α + k - 1) k.
- Defined in
- Mathlib.Data.Sym.Card
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 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.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement and proof · cited by 1,386
- Nat.choosestatement and proof · cited by 494
- Symstatement and proof · cited by 150
- Sym.card_sym_eq_multichooseproof · cited by 3
- Nat.multichoose_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finset.card_finsuppAntidiag_nat_eq_chooseproof · cited by 0