# isShelling -- determines whether a list of faces is a shelling

## Synopsis

• Usage:
isShelling L
• Inputs:
• L, a list, a list of faces (i.e., squarefree monic monomials)
• Outputs:
• B, , true if and only if $L$ is shelling

## Description

Determines if a list of faces is a shelling order of the simplicial complex generated by the list.

Let $S$ be the simplicial complex generated by the list of facets $L$. If $S$ is pure, then definition III.2.1 in [St] is used. That is, $L_1, .., L_n$ is a shelling order of $S$ if 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, $L_1, .., L_n$ is a shelling order if the intersection of the faces of the first $j-1$ facets with the faces of the $L_j$ is pure and $dim L_j - 1$-dimensional.

 i1 : R = QQ[a..e]; i2 : isShelling {a*b*c, b*c*d, c*d*e} o2 = true i3 : isShelling {a*b*c, c*d*e, b*c*d} o3 = false