Lambda-determinants and domino-tilings

James Propp

Consider the $2n$-by-$2n$ matrix $M=(m_{i,j}{)}_{i,j=1}^{2n}$ with $m_{i,j}=1$ for $i,j$ satisfying $|2i-2n-1|+|2j-2n-1|\le 2n$ and $m_{i,j}=0$ for all other $i,j$, consisting…