3 problems

Pemantle's conjecture. CNC implies CNA. In particular, the equivalent formulation considered here is that $R^+$ implies CNA.

Let $\beta>0$, and for distinct edges write $\mathbb{P}_{\beta}[e_1,\ldots,e_k]$ for the probability that all listed edges occur in the forest. Negative association conjecture. For…

Let $\mathcal G$ be a graph, and let $e$ and $f$ be distinct edges. Write $G=F(\mathcal G;\mathbf y)$ for the generating polynomial of its spanning forests, and let $\mathscr S$ be…