On partitioning of hypergraphs

We study edge-isoperimetric problems (EIP) for hypergraphs and extend some technique in this area from graphs to hypergraphs. In particular, we establish some new results on a relationship between the EIP and some extremal poset problems, and apply them to obtain an exact solution of the EIP for certain hypergraph families. We also show how to solve the EIP on hypergraphs in some cases when the link to posets does not work. Another outcome of our results is a new series of hypergraphs admitting nested solutions in the EIP.