# isShelling -- determines whether a list represents a shelling of a simplicial complex.

## Synopsis

• Usage:
b = isShelling(P)
• Inputs:
• P, a list, A list of lists of integers. Each list of integers is a facet of the complex and the order is a possible shelling.
• Outputs:
• b, , true if and only if P is a shelling.

## Description

An ordering $F_1,..F_d$ of the facets of a simplicial complex $P$ is shellable if $(F_1 \cup .. \cup F_{k-1}) \cap F_k$ is pure of dim$F_k -1$ for all $k = 2,..,d$. Determines if a list of faces is a shelling order of the simplicial complex.

 i1 : P = {{1, 2, 3}, {1, 2, 5}}; i2 : isShelling(P) o2 = true i3 : Q = {{1,2,3},{3,4,5},{2,3,4}}; i4 : isShelling(Q) o4 = false

## Ways to use isShelling :

• "isShelling(List)"

## For the programmer

The object isShelling is .