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isShellable -- determines whether a simplicial complex is shellable



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 $F_1, ..., F_n$ so that the difference in the $j$-th and $j-1$-th subcomplex has a unique minimal face, for $2 \leq j \leq n$.

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 $F_1, .., F_n$ such that the intersection of the faces of the first $j-1$ with the faces of the $F_j$ is pure and $dim F_j - 1$-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 :

For the programmer

The object isShellable is a method function.