6 problems

Let $G$ and $G_0$ satisfy the assumptions of the theorem preceding this statement, and let $h_G(p)$ and $h_{G_0}(p)$ denote their monomer–dimer entropies at density $p$. Entropy ma…

Let $\{G_k=(V_k,E_k)\}_{k\in\mathbb{N}}$ be a sequence of $r$-regular bipartite graphs with $\#V_k\to\infty$. Let $h_{\{G_k\}}(p)$ denote the associated monomer–dimer entropy, and…

Coefficient-sign conjecture. The coefficients satisfy $a_j > 0$ and $b_j < 0$ for all $j \geqslant 2$. This sign pattern would make truncations of the first expansion lower bounds…

Convergence conjecture. The series for $\lambda_d(p)$ is convergent for

Positivity conjecture. For hypercubic lattices, all expansion coefficients $a_k(d)$ are positive.

Master Algebraic Conjecture. The two expressions are equivalent as formal sums.