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SimplicialDecomposability :: isShellable

isShellable -- determines whether a simplicial complex is shellable

Synopsis

Description

The pure and non-pure cases are handled separately. If S is pure, then definition III.2.1 in [St] is used. That is, S is shellable if its facets can be ordered F1, ..., Fn so that the difference in the j-th and j-1-th subcomplex has a unique minimal face, for 2 ≤j ≤n.

If S is non-pure, then definition 2.1 in [BW-1] is used. That is, a simplicial complex S is shellable if the facets of S can be ordered F1, .., Fn such that the intersection of the faces of the first j-1 with the faces of the Fj is pure and dim Fj - 1-dimensional.
i1 : R = QQ[a..f];
i2 : isShellable simplicialComplex {a*b*c*d*e}

o2 = true
i3 : isShellable simplicialComplex {a*b*c, c*d*e}

o3 = false
i4 : isShellable simplicialComplex {a*b*c, b*c*d, c*d*e}

o4 = true
i5 : isShellable simplicialComplex {a*b*c, c*d, d*e, e*f, d*f}

o5 = true
i6 : isShellable simplicialComplex {a*b*c, c*d, d*e*f}

o6 = false

See also

Ways to use isShellable :