  We study thresholds for the appearance of a 2-core in random hypergraphs that
are a mixture of a constant number of random uniform hypergraphs each with a
linear number of edges but with different edge sizes. For the case of two
overlapping hypergraphs we give a solution for the optimal (expected) number of
edges of each size such that the 2-core threshold for the resulting mixed
hypergraph is maximized. We show that for adequate edge sizes this threshold
exceeds the maximum 2-core threshold for any random uniform hypergraph, which
can be used to improve the space utilization of several data structures that
rely on this parameter.
