The hypergraph shadow 
,
or simply shadow, of an 
-uniform hypergraph 
is the 
-uniform hypergraph consisting
of all 
-element
subsets contained in at least one hyperedge
of 
,
namely
 |
More generally, for 
,
the 
-shadow
consists of the 
-element
subsets contained in the hyperedges
of 
.
Hypergraph shadows are central in extremal set theory. The shadow bound proving Kalai's conjecture is one example.
