Theorems · Definition · group theory
CoxeterSystem.length
{B : Type u_1} → {W : Type u_2} → [inst : Group W] → {M : CoxeterMatrix B} → CoxeterSystem M W → W → ℕThe length of w; i.e., the minimum number of simple reflections that
must be multiplied to form w.
- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- CoxeterMatrixstatement and proof · cited by 140
- Nat.findproof · cited by 139
- CoxeterSystemstatement and proof · cited by 126
Cited by46
Results whose statement or proof uses this declaration.
- CoxeterSystem.IsReducedproof · cited by 19
- CoxeterSystem.length_wordProd_lestatement · cited by 9
- CoxeterSystem.IsLeftDescentproof · cited by 8
- CoxeterSystem.IsRightDescentproof · cited by 8
- CoxeterSystem.length_invstatement and proof · cited by 7
- CoxeterSystem.IsRightInversionproof · cited by 7
- CoxeterSystem.IsLeftInversionproof · cited by 6
- CoxeterSystem.lengthParity_eq_ofAdd_lengthstatement · cited by 5
- CoxeterSystem.length_simplestatement and proof · cited by 5
- CoxeterSystem.length_mul_lestatement and proof · cited by 3
- CoxeterSystem.length_mul_simplestatement and proof · cited by 3
- CoxeterSystem.length_onestatement · cited by 3