Interchange Theorems for Hypergraphs and Factorization of Their Degree Sequences

The aim of this paper is to unify interchange theorems and extend them to hypergraphs. To this end sufficient conditions for equality of thel1-distance between equivalence classes and thel1-distance between corresponding order-type functions are provided. The generality of this result is demonstrated by a number of new corollaries concerning the factorization and the switching completeness of degree sequences of graphs and hypergraphs.