EL-labelings and canonical spanning trees for subword complexes
نویسندگان
چکیده
SUBWORD COMPLEXES (W,S) finite Coxeter system, Q = q1q2 · · · qm ∈ S∗, and ρ ∈W . Subword complex SC(Q, ρ) = simplicial complex with • vertices = [m] = positions in Q, • facets =F(Q, ρ) = complements of reduced expressions of ρ in Q. Exm. Q = τ2τ3τ1τ3τ2τ1τ2τ3τ1 in (S4, {(i i+ 1)}) ρ = [4, 1, 3, 2] = τ2τ3τ2τ1 = τ3τ2τ3τ1 = τ3τ2τ1τ3 F(Q, ρ) = {1, 2, 3, 5, 6}, {1, 2, 3, 6, 7}, {1, 2, 3, 7, 9}, {1, 3, 4, 5, 6}, {1, 3, 4, 6, 7}, {1, 3, 4, 7, 9}, . . . Inductive structure: if Qa = q1 · · · qm−1, then F(Q, ρ) = F(Qa, ρqm) t ( F(Qa, ρ) ?m ) .
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