5 problems

Let $C_{m,n}$ be the square-grid cylinder, let $Z(C_{m,n})$ be the hard-particle partition function at activity $-1$, and suppose that $n$ is odd. Jonsson's cylinder partition-func…

Let $m$ and $n$ be relatively prime, and consider the hard-square model on a square grid with toroidal identifications. For its independent sets $\sigma$, form the alternating sum…

Consider the hard-square model at activity $-1$ on a square grid with toroidal identifications, and let $T$ be the associated transfer matrix. Let $P(t)=\det(tI-T)$ be its characte…

Let $C_{m,n}$ be the square-grid cylinder with vertices $(i,j)$ for $1\leq i\leq m$ and $1\leq j\leq n$, with horizontal grid edges and the identifications joining $(i,1)$ to…

Let $m$ and $n$ be positive integers, and consider the hard-square model on an $m\times n$ square grid with doubly periodic, or toroidal, boundary conditions. Its partition functio…