Theorems · Theorem · group theory
Equiv.Perm.parts_partition
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α},
σ.partition.parts = σ.cycleType + Multiset.replicate (Fintype.card α - σ.support.card) 1- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 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.
- Fintypestatement and proof · cited by 7,736
- Multisetstatement · cited by 2,627
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Multiset.replicatestatement · cited by 88
- Equiv.Perm.cycleTypestatement · cited by 87
- Nat.Partition.partsstatement · cited by 28
- Equiv.Perm.partitionstatement · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.filter_parts_partition_eq_cycleTypeproof · cited by 1
- Equiv.Perm.partition_eq_of_isConjproof · cited by 0