Theorems · Theorem · group theory
Equiv.Perm.sign_of_cycleType
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (f : Equiv.Perm α),
Equiv.Perm.sign f = (-1) ^ (f.cycleType.sum + f.cycleType.card)- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 101 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- mul_oneproof · cited by 3,885
- MonoidHomstatement · cited by 3,629
- Unitsstatement and proof · cited by 2,804
- Multisetproof · cited by 2,627
- mul_assocproof · cited by 1,667
- Equiv.Permstatement and proof · cited by 1,375
- pow_oneproof · cited by 894
- Multiset.mapproof · cited by 876
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
Cited by7
Results whose statement or proof uses this declaration.
- AlternatingGroup.map_subtype_of_cycleTypeproof · cited by 3
- Equiv.Perm.closure_cycleType_eq_two_two_eq_alternatingGroupproof · cited by 2
- Equiv.Perm.IsThreeCycle.signproof · cited by 1
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1
- Equiv.Perm.cycleType_eq_two_two_subset_alternatingGroupproof · cited by 1
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0