Theorems · Theorem · group theory
Equiv.Perm.sum_cycleType
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (σ : Equiv.Perm α), σ.cycleType.sum = σ.support.card- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 100 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.
Cites17
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
- Multisetproof · cited by 2,627
- Finset.cardstatement and proof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.sumstatement and proof · cited by 388
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.IsCycleproof · cited by 108
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- Equiv.Perm.Disjointproof · cited by 81
- Multiset.sum_singletonproof · cited by 26
- Equiv.Perm.Disjoint.cycleType_mulproof · cited by 14
- Equiv.Perm.IsCycle.cycleTypeproof · cited by 12
Cited by14
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.card_supportproof · cited by 6
- Equiv.Perm.card_fixedPointsproof · cited by 4
- card_support_eq_three_iffproof · cited by 3
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- Equiv.Perm.exists_with_cycleType_iffproof · cited by 2
- Equiv.Perm.card_le_of_centralizer_le_alternatingproof · cited by 1
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1
- Equiv.Perm.le_card_support_of_mem_cycleTypeproof · cited by 1
- Equiv.Perm.two_dvd_card_supportproof · cited by 1
- Equiv.Perm.isCycle_of_prime_orderproof · cited by 1
- Equiv.Perm.sum_cycleType_leproof · cited by 1
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1