10 problems

Let $P$ and $Q$ be patterns, and let $P\otimes Q$ denote their Kronecker product. Write $\operatorname{sat}(n,P)$ for the square saturation function and $\operatorname{ssat}(n,Q)$…

Let $A\in\mathbb{R}_{+}^{m\times n}$ be a nonnegative matrix, where $\operatorname{rk}(A)$ denotes its ordinary rank and $\operatorname{rk}_{+}(A)$ its nonnegative rank. Vandaele–G…

Let $A_1$ and $A_2$ be nonnegative matrices. Dagstuhl multiplicativity conjecture. It was conjectured that … This conjecture was later disproved by constructing nonnegative matrice…

For $n\ge10$, let $P(n)$ be the set of partitions of $n$, and let $[\lambda]$ denote the irreducible character of $S_n$ indexed by $\lambda$. Refinement of the HSTZ conjecture. The…

For $n\ne2,4,9$, let $P(n)$ denote the set of partitions of $n$, and let $[\lambda]$ be the irreducible character of $S_n$ indexed by $\lambda\in P(n)$. Heide–Saxl–Tiep–Zalesski co…

Let $n=\tfrac{1}{2}k(k+1)$ and let $\rho_k=(k,\ldots,2,1)\vdash n$ be the staircase partition. Write $S^2([\rho_k])$ and $A^2([\rho_k])$ for the symmetric and alternating parts of…

Let $\Lambda_n$ be the ring of homogeneous symmetric functions of degree $n$ with Kronecker product $*$, and define … where $s_\lambda$ is the Schur function indexed by $\lambda$.…

Let $d$ be a positive integer, let $\ol\nu\vdash d$, and let $s_{\ol\nu}(x)$ be the polynomial map associated with the staircase Kronecker-square coefficients. Let $c(\ol\nu)$ be t…

Let $d$ be a positive integer, let $\ol\nu\vdash d$, and let $s_{\ol\nu}$ be the polynomial map associated with the staircase Kronecker-square coefficients. Let $c(\ol\nu)$ and…

Let $U$ be a unitary matrix with a fixed Kronecker product structure, meaning that the sequence of sizes of its Kronecker factors is fixed up to order. In either of the two cases c…