Theorems · Definition · group theory
CoxeterSystem.wordProd
{B : Type u_1} → {W : Type u_3} → [inst : Group W] → {M : CoxeterMatrix B} → CoxeterSystem M W → List B → WThe product of the simple reflections of W corresponding to the indices in ω.
- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 82 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
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.simpleproof · cited by 73
Cited by43
Results whose statement or proof uses this declaration.
- CoxeterSystem.IsReducedproof · cited by 19
- CoxeterSystem.wordProd_nilstatement · cited by 11
- CoxeterSystem.length_wordProd_lestatement and proof · cited by 9
- CoxeterSystem.wordProd_consstatement · cited by 9
- CoxeterSystem.exists_isReducedstatement and proof · cited by 8
- CoxeterSystem.length_invproof · cited by 7
- CoxeterSystem.lengthParity_eq_ofAdd_lengthproof · cited by 5
- CoxeterSystem.wordProd_appendstatement · cited by 5
- CoxeterSystem.wordProd_singletonstatement · cited by 5
- CoxeterSystem.wordProd_reversestatement and proof · cited by 4
- CoxeterSystem.length_mul_leproof · cited by 3
- CoxeterSystem.getD_leftInvSeqstatement and proof · cited by 3