Recurrence Relations for Steiner Systems with \(t = 2\)

Abstract

A Steiner system \(S(2, k, v)\) is a collection of \(k\)-subsets (blocks) of a \(k\)-set \(V\) such that each \(2\)-subset of \(V\) is contained in exactly one block. We find re-currence relations for \(S(2, k, v)\).