10 problems

Let $T_{L,L}$ be the diagonal transfer-matrix sub-block for a triangular-lattice strip of width $L$ with fully toroidal boundary conditions, and let $b^{(L)}_1$ denote the stated a…

For a zero-temperature triangular-lattice Potts antiferromagnet on toroidal strips, let $q_0(L)$ and $q_2(L)$ be the relevant real crossings, and let $\ell$ denote the number of br…

Let $q_2(L)$ denote the crossing of the two largest eigenvalues in the $\ell=2$ sector for a triangular-lattice strip of width $L$ with fully periodic boundary conditions, and let…

Let $q_0(L)$ denote the crossing for a triangular-lattice strip of width $L$ with fully periodic boundary conditions, and let $q_{\rm B}\simeq3.8196717312$ be the value where Baxte…

Let $q_0(L)$ denote the relevant real crossing for a triangular-lattice strip of width $L$ with fully periodic boundary conditions. Triangular-lattice 3p ± 1 conjecture. For all wi…

For a zero-temperature square-lattice Potts antiferromagnet on toroidal strips, let $q$ be the Potts parameter, let $q_0(L)$ be the relevant real crossing, and let $\ell$ denote th…

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions, and let $q_{\rm c}(\mathrm{sq})=3$…

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions. Odd-width square-lattice conjectur…

Harary almost-completeness conjecture. There is no Harary polynomial which is almost complete for $\mathbb{G}(n,1/2)$.

Bollobás–Pebody–Riordan conjecture. For the model with $p(n)=1/2$, the chromatic polynomial is almost complete.