Symmetric 2-Designs We just proved that for any symmetric 2-design (or Symmetric BIBDs as most literature puts it) with parameters $(v,k,\lambda)$, any two blocks intersects at exactly $\lambda$ points. Our lecturer noted in passing that the converse holds true, but I can't seem to prove it. Wiki says "a theorem of Ryser provides the converse".
Would someone be so kind to provide (or give reference) a proof of this? And note that I'm only doing a first course on algebraic combinatorics so if this converse turns out to be some theorem way harder just let me know as well.
Thanks!

We can show this by considering the dual structure, that is, the structure obtained by reversing the role of "points" and "blocks".  If the original design $\mathcal{D}$ has the property that any two blocks share precisely $\lambda$ points, then the dual structure $\mathcal{D}^{T}$ satisfies the requirements to be a design.  The fact that $\mathcal{D}$ is symmetric then follows from the fact that a design has at least as many blocks as points (applied to both $\mathcal{D}$ and $\mathcal{D}^{T}$). This last result is a generalization of Fisher's inequality.
