Symmetric hypergraph theorem

The Symmetric Hypergraph Theorem is a result in the field of combinatorics, particularly in the study of hypergraphs. A hypergraph is a generalization of a graph where an edge (called a hyperedge) can connect any number of vertices, not just two. The theorem itself often pertains to specific properties of hypergraphs that exhibit a certain type of symmetry, particularly focusing on the existence of particular structures within these hypergraphs.