  Imposing a strong condition on the linear order of shellable complexes, we
introduce strong shellability. Basic properties, including the existence of
dimension-decreasing strong shelling orders, are developed with respect to
nonpure strongly shellable complexes. Meanwhile, pure strongly shellable
complexes can be characterized by the corresponding codimension one graphs. In
addition, we show that the facet ideals of pure strongly shellable complexes
have linear quotients.

Combinatorics