# isSheddingFace -- determines whether a face of a simplicial complex is a shedding face

## Synopsis

• Usage:
isSheddingFace(F, S)
• Inputs:
• F, , a face of $S$
• S, ,
• Outputs:
• B, , true if and only if $F$ is a shedding face of $S$

## Description

Definition 3.1 in [Wo] states that a face $F$ of a simplicial complex $S$ is a shedding face if every face $G$ of the star of $S$ by $F$ satisfies the exchange property, that is, for every vertex $v$ of $F$ there is a vertex $w$ of the face deletion of $S$ by $G$ such that $(G \cup w) \setminus v$ is a face of $S$.

 i1 : R = QQ[a..e]; i2 : T = simplicialComplex {a*b*c, b*c*d, c*d*e}; i3 : isSheddingFace(b*d, T) o3 = true i4 : isSheddingFace(b*c*d, T) o4 = false

• faceDelete -- computes the face deletion for a simplicial complex
• isDecomposable -- determines whether a simplicial complex is k-decomposable
• isShellable -- determines whether a simplicial complex is shellable
• isVertexDecomposable -- determines whether a simplicial complex is vertex-decomposable