Hierarchical representations, as irregular pyramids, are the bases of several applications in the field of discrete imagery. So, n-dimensional "bottom-up" irregular pyramids can be defined as stacks of successively reduced n-dimensional generalized maps (n-G-maps) [13], each n-G-map being defined from the previous level by using removal and contraction operations defined in [18]. Our goal is to build a theoretical framework for the definition and handling of n-dimensional "top-down" irregular pyramids. To do that, we propose in this paper to study the definition of insertion and expansion operations that allows to conceive this kind of pyramids.