(a) a
family of
finite sets, closed under
subsets.
(b) a collection of
simplices meeting
face-to-face.
The first type of
complex can be made into the second, by
embedding the members of the
sets in
general position in some
space of suffiently high
dimension, and forming
simplices by taking the
convex hull of each
set. The
sets of a
simplicial complex are also known as
faces.
--back to
combinatorics--