  A family F of permutations of the vertices of a hypergraph H is called
"pairwise suitable" for H if, for every pair of disjoint edges in H, there
exists a permutation in F in which all the vertices in one edge precede those
in the other. The cardinality of a smallest such family of permutations for H
is called the "separation dimension" of H and is denoted by \pi(H).
Equivalently, \pi(H) is the smallest natural number k so that the vertices of H
can be embedded in R^k such that any two disjoint edges of H can be separated
by a hyperplane normal to one of the axes. We show that the separation
dimension of a hypergraph H is equal to the "boxicity" of the line graph of H.
This connection helps us in borrowing results and techniques from the extensive
literature on boxicity to study the concept of separation dimension.
