Shelling (topology)


In mathematics, a shelling of a simplicial complex is a way of gluing it together from its maximal simplices in a well-behaved way. A complex admitting a shelling is called shellable.

Definition

A d-dimensional simplicial complex is called pure if its maximal simplices all have dimension d. Let be a finite or countably infinite simplicial complex. An ordering of the maximal simplices of is a shelling if the complex
is pure and of dimension for all. That is, the "new" simplex meets the previous simplices along some union of top-dimensional simplices of the boundary of. If is the entire boundary of then is called spanning.
For not necessarily countable, one can define a shelling as a well-ordering of the maximal simplices of having analogous properties.

Properties