  We study the distribution of maximal-chain lengths between two elements of a
causal set and its relationship with the embeddability of the causal set in a
region of flat spacetime. We start with causal sets obtained from uniformly
distributed points in Minkowski space. After some general considerations we
focus on the 2-dimensional case and derive a recursion relation for the
expected number of maximal chains $n_k$ as a function of their length $k$ and
the total number of points $N$ between the maximal and minimal elements. By
studying these theoretical distributions as well as ones generated from
simulated sprinklings in Minkowski space we identify two features, the most
probable path length or peak of the distribution $k_0$ and its width $\Delta$,
which can be used both to provide a measure of the embeddability of the causal
set as a uniform distribution of points in Minkowski space and to determine its
dimensionality, if the causal set is manifoldlike in that sense. We end with a
few simple examples of $n_k$ distributions for non-manifoldlike causal sets.
