4 problems

Diagonalizing sequence conjecture. For every $U_0\in\operatorname{U}(2)$, the sequences satisfy

Let $U(d)$ denote a Haar-random $d\times d$ unitary matrix, and let $t$ be a positive integer. Hunter-Jones's conjecture. The permanent moment satisfies … The source attributes thi…

An almost Hadamard matrix in the complex sense is the notion introduced in the cited work, while a complex Hadamard matrix is a unitary matrix whose entries have equal modulus afte…

Let $d$ and $k$ be fixed, let ${\bf v}^{(1)},\ldots,{\bf v}^{(k)}$ be fixed vectors, and let $U$ vary over unitary matrices. Write ${\mathcal V}$ for the associated variety and let…