Theorems · Theorem · group theory
Equiv.Perm.card_of_cycleType_singleton
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {n : ℕ},
2 ≤ n → n ≤ Fintype.card α → {g | g.cycleType = {n}}.card = (n - 1).factorial * (Fintype.card α).choose nThe number of cycles of given length
- Defined in
- Mathlib.GroupTheory.Perm.Centralizer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- mul_oneproof · cited by 3,885
- Finset.univstatement and proof · cited by 3,473
- Multisetstatement · cited by 2,627
- Finset.cardstatement and proof · cited by 2,327
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- Fintype.cardstatement and proof · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- Finset.filterstatement and proof · cited by 949
- Finset.prod_congrproof · cited by 646
- Nat.factorialstatement and proof · cited by 616
Cited by1
Results whose statement or proof uses this declaration.
- AlternatingGroup.card_of_cycleType_singletonproof · cited by 0