Counting lattice triangulations: Fredholm equations in combinatorics

S. Yu. Orevkov

Let $f(m,n)$ be the number of primitive lattice triangulations of $m\times n$ rectangle. We compute the limits ${\lim }_{n}f(m,n{)}^{1/n}$ for $m=2$ and $3$. For $m=2$ we obtain the exac…