A simplex-cluster of dimension 
in a family of 
-element sets is a collection of 
distinct members whose total intersection
is the empty set, every 
of whose members have nonempty intersection,
and whose union has at most 
elements (Wu and Feng 2026). This is usually called a 
-simplex-cluster.
The Keevash-Mubayi simplex-cluster conjecture gives the largest size of a family with no such collection. Here simplex refers to this intersection pattern, not to a geometric simplex.
