Vertex-decomposability is just zero-decomposability when $S$ is pure, see [PB]. When $S$ is non-pure, [BW-2] gives a generalisation: A complex $S$ is vertex decomposable if it is either a simplex or there exists a shedding vertex.
i1 : R = QQ[a..f]; |
i2 : isVertexDecomposable simplicialComplex {a*b*c*d*e} o2 = true |
i3 : isVertexDecomposable boundary simplicialComplex {a*b*c*d*e} o3 = true |
i4 : isVertexDecomposable simplicialComplex {a*b*c, c*d*e} o4 = false |
i5 : isVertexDecomposable simplicialComplex {a*b*c, c*d, d*e, e*f, d*f} o5 = true |
Whether the complex is vertex-decomposable is cached.
The object isVertexDecomposable is a method function.