Theorems · Theorem · group theory
Equiv.Perm.cycleType_def
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (σ : Equiv.Perm α),
σ.cycleType = Multiset.map (Finset.card ∘ Equiv.Perm.support) σ.cycleFactorsFinset.val- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 92 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Multisetstatement · cited by 2,627
- Finset.cardstatement · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.mapstatement · cited by 876
- Finset.valstatement · cited by 438
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.cycleFactorsFinsetstatement · cited by 96
- Equiv.Perm.cycleTypestatement · cited by 87
Cited by7
Results whose statement or proof uses this declaration.
- Equiv.Perm.Disjoint.cycleType_mulproof · cited by 14
- Equiv.Perm.OnCycleFactors.odd_of_centralizer_le_alternatingGroupproof · cited by 2
- Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinsetproof · cited by 1
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_oneproof · cited by 1
- Equiv.Perm.cycleType_eq'proof · cited by 1
- Equiv.Perm.centralizer_le_alternating_iffproof · cited by 0