  Let $R_1$ be a commutative ring, let $R_2$ be a finitely generated extension
ring of $R_1$, and let $S$ be a ring that is intermediate between $R_1$ and
$R_2$. For $R_1 = R[x]$ and $R_2 = R[x,y]$, this paper gives simple
combinatorial constructions of intermediate rings $S$ that are not finitely
generated over $R[x]$.
