7 problems

Let $\lambda'$ be a two-row partition, and let $\mathrm{prs}_{\lambda'}$ be the associated skew Schur partition function, defined on those partitions for which the function is defi…

Let $M$ be a dimension, and let $U_1$, $U_2$, and $U_3$ be unitary matrices. In phase retrieval, an intensity-measurement operator is formed as $\Phi=[U_1~U_2~U_3]$. Wright's conje…

For a positive integer $k$, let $\mathrm{pre}_k$ be the elementary symmetric partition function, and let $\mathcal{P}_{>k}(n)$ denote the set of partitions of $n$ with length stric…

Let $n$ and $k$ be positive integers, and let $\mathrm{pre}_k$ map a partition with at least $k$ parts to the summands of the elementary symmetric polynomial $e_k$ evaluated at its…

Let $F:\mathbb{R}^n\rightarrow\mathbb{R}^n$ be a $C^1$ map. Suppose there exists an $\varepsilon>0$ such that $|\lambda|\geqslant\varepsilon$ for every eigenvalue $\lambda$ of…

Let $F$ be a simply switched piecewise linear function, meaning that it has an abs-normal representation of switching depth $nu=1$. A map is open if it maps open sets to open sets,…

Let $\Phi$ be the measurement matrix for signals in $\mathbb{C}^M$, with $N$ intensity measurements, and write $\mathrm{AlmInj}[\Phi,\mathbb{C}^{M\times N}]$ for almost injectivity…