A generalized hypergraph 4-cycle is an 
-uniform hypergraph consisting
of four distinct hyperedges 
, 
, 
, and 
such that 
and 
.
Let 
be the maximum number of hyperedges in an 
-vertex 
-uniform hypergraph containing
no generalized hypergraph 4-cycle. Huang et al. (2026) proved that, for every
fixed 
and all sufficiently large 
,
 |
where 
is the floor function. Every extremal example is
a full 
-uniform
star together with a maximum-cardinality collection of pairwise disjoint hyperedges
on the other 
vertices, called a matching.
When 
,
a second type is obtained by deleting the star hyperedge
through the 
unmatched noncentral vertices
and adding the 
-set formed by these vertices
and one graph vertex from the matching. The corresponding
problem for 
remains open.
