  In this paper, we present an equitable partition theorem of tensors, which
gives the relations between $H$-eigenvalues of a tensor and its quotient
equitable tensor and extends the equitable partitions of graphs to hypergraphs.
Furthermore, with the aid of it, some properties and $H$-eigenvalues of the
generalized power hypergraphs are obtained, which extends some known results,
including some results of Yuan, Qi and Shao.
