  Building on the theory of causal discovery from observational data, we study
interactions between multiple (sets of) random variables in a linear structural
equation model with non-Gaussian error terms. We give a correspondence between
structure in the higher order cumulants and combinatorial structure in the
causal graph. It has previously been shown that low rank of the covariance
matrix corresponds to trek separation in the graph. Generalizing this criterion
to multiple sets of vertices, we characterize when determinants of subtensors
of the higher order cumulant tensors vanish. This criterion applies when hidden
variables are present as well. For instance, it allows us to identify the
presence of a hidden common cause of k of the observed variables.
