3 problems

Let $G=(V,E)$ be the adjacency graph of a uniformly repetitive (or uniformly recurrent) rhombus tiling. Let $F$ be a percolation process, monotone and freezing, on configurations…

Let $D_{s,t}(n)$ denote the determinant associated with the corresponding family of cyclically symmetric rhombus-tiling regions, with the parity of $s-t$ distinguishing ordinary ti…

Let $\mu$ be an indeterminate, let $n\geqslant1$ and $r\geqslant0$ be integers, and define the rising factorial $(a)_k=a(a+1)\cdots(a+k-1)$. Let $D_{-1,2r}(2n)$ be the determinant…