3 problems

Finite-generation conjecture. The cone $C$ is $(R,G)$-finitely generated if and only if there exists $A\in\mathbb{Q}^{n\times n}$ and $\lambda_1,\dots,\lambda_n\in\mathbb{R}_{>0}$…

Growth conjecture for $bmu_d$. It has been conjectured that

Cyclically distinct composition conjecture. The number of integer points $\lambda\in\mathcal{C}_n$ with $\lambda_0=m$ is equal to the number of compositions of $m$ into $n$ parts t…