Exact enumeration of lozenge tilings of a triangular region

Jun Yan

We prove that the number of lozenge tilings of a certain triangular region ${\mathcal{T}}_n$ is given by the formula \[T_n=\prod_{\substack{1\leq a<b\leq 3n+2\\(a,b)\not=(n+1,2n+2)}}…