6 problems

Direct-sum conjecture for transversal q-matroids. The direct sum $M_1\oplus M_2$ is a transversal $q$-matroid with presentation $\mathcal{X}_1\oplus\mathcal{X}_2$.

Let $p\in [1,\infty)$, let $d\in\mathbb{Z}_{\geq 2}$, let $A\subseteq\mathcal{L}(L^p(\mu_0))$ be an $L^p$ operator algebra with a contractive approximate identity, and for each…

A well-quasi-order (wqo) is a quasi-ordered class in which every infinite sequence contains indices $i<j$ with the $i$th element below the $j$th. Let…

Let a DSC be a direct sum of chains, and let $Sib(\mathcal{D})$ denote its sibling number. Suppose … is a countable DSC, where $\mathcal{D}_1$ is bounded, $\mathcal{D}_2$ is a non-…

Multidimensional direct sum conjecture. The rank of $d$-dimensional tensors is additive with respect to direct sums:

For each $n$, let $L_n$ be the minimal-order linear differential operator for $\tilde{\chi}^{(n)}$. A direct-sum decomposition means that the operator for a higher-particle contrib…