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Theorems · Inductive type · group theory

Equiv.Perm.Basis

{α : Type u_1} → [DecidableEq α] → [Fintype α] → Equiv.Perm α → Type u_1

A Basis of a permutation is a choice of an element in each of its cycles

Defined in
Mathlib.GroupTheory.Perm.Centralizer
Cited by
25 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
DecidableEqFintype
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Equiv.Perm.Basis.ofPermHomFun · cited by 9Basis.ofPermHomFunEquiv.Perm.Basis.mem_support_self · cited by 6Basis.mem_support_selfEquiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eq · cited by 5Basis.mem_fixedPoints_or_…Equiv.Perm.Basis.ofPermHomFun_apply_of_cycleOf_mem · cited by 5Basis.ofPermHomFun_apply_…Equiv.Perm.Basis.ofPermHomFun_apply_of_mem_fixedPoints · cited by 5Basis.ofPermHomFun_apply_…Equiv.Perm.Basis.toCentralizer · cited by 5Basis.toCentralizerEquiv.Perm.Basis.ofPermHom · cited by 4Basis.ofPermHomEquiv.Perm.OnCycleFactors.mem_range_toPermHom_iff · cited by 3OnCycleFactors.mem_range_…Equiv.Perm.Basis.nonempty · cited by 2Basis.nonemptyEquiv.Perm.Basis.ofPermHomFun_commute_zpow_apply · cited by 2Basis.ofPermHomFun_commut…Equiv.Perm.Basis.sameCycle · cited by 2Basis.sameCycleEquiv.Perm.count_le_one_of_centralizer_le_alternating · cited by 1Perm.count_le_one_of_cent…Equiv.Perm.Basis.card_ofPermHom_support · cited by 1Basis.card_ofPermHom_supp…Equiv.Perm.Basis.injective · cited by 1Basis.injectiveEquiv.Perm.Basis.mem_support_self' · cited by 1Basis.mem_support_self'Fintype · cited by 7736FintypeEquiv.Perm · cited by 1375Equiv.PermPerm.BasisCITED BYCITES

Cites2

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Cited by35

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