3 problems

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…

Let $D_{1,1}(n)$ be the determinant appearing below, with $\binom{\bullet}{\bullet}$ denoting a binomial coefficient, $\binom{\bullet}{\bullet}$ and $\binom{\bullet}{\bullet}$ inte…