Theorems · Definition · group theory
Equiv.Perm.cycleType
{α : Type u_1} → [Fintype α] → [DecidableEq α] → Equiv.Perm α → Multiset ℕThe cycle type of a permutation
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Multisetstatement · cited by 2,627
- Finset.cardproof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- Equiv.Perm.supportproof · cited by 230
- Equiv.Perm.cycleFactorsFinsetproof · cited by 96
Cited by90
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycleproof · cited by 34
- Equiv.Perm.sum_cycleTypestatement and proof · cited by 14
- Equiv.Perm.Disjoint.cycleType_mulstatement and proof · cited by 14
- Equiv.Perm.IsCycle.cycleTypestatement · cited by 12
- alternatingGroup.kleinFourproof · cited by 11
- Equiv.Perm.cycleType_onestatement · cited by 9
- Equiv.Perm.sign_of_cycleTypestatement and proof · cited by 7
- Equiv.Perm.lcm_cycleTypestatement and proof · cited by 7
- Equiv.Perm.cycleType_defstatement · cited by 7
- Equiv.Perm.two_le_of_mem_cycleTypestatement and proof · cited by 6
- Equiv.Perm.IsThreeCycle.cycleTypestatement · cited by 5
- Equiv.Perm.cycleType.congr_simpstatement and proof · cited by 5