5 problems

Minimality for $\textnormal{E}_{\textnormal{BPD}}$ in general. For all $N\in\mathbb N\backslash\{0,1\}$, we have

Let $V$ be a stable pair potential with stability constant $B$, and let ${\rm\bf m}$ be the Penrose partition scheme. For $n\geq 2$, let $T_n$ be the set of trees on $n$ labelled v…

Ruelle-potential decomposition conjecture. Any stable and tempered pair potential can always be written as a sum of a non-negative potential plus an absolutely summable stable pote…

Ruelle's decomposition conjecture. Any stable and tempered potential could always be written via such a decomposition.

Ruelle-type decomposition conjecture. The class of Ruelle potentials actually coincides with the whole class of stable and tempered potentials.