11 problems

Unique-norm integral Fourier matrix conjecture. Then

Let $G$ be a finite reductive group with generalized Frobenius map $F$, let $\boldsymbol{G}$ be the corresponding algebraic group, and let $\boldsymbol{G}^{F^{\delta}}$ and…

Square-free Fourier principal-minor conjecture. If $N$ is square-free, then all principal minors of ${\mathcal{F}}_N$ are nonzero.

Column-permutation conjecture. For every natural number $N$, there exists a permutation $\sigma$ such that the Fourier matrix with permuted columns has no zero principal minors.

Let $q\geq3$ be prime, let $K\in M_{M\times N}(\mathbb C)$ be an isolated truncation of $F_p$ with $p$ prime, and let $S,T$ be the sets used in Theorem 4.4. That theorem constructs…

A square master Hadamard matrix is a master Hadamard matrix of square size, and $F_p$ denotes the Fourier matrix of prime order $p$. A matrix is isolated when it has no nontrivial…

In the square case, a master Hadamard matrix is a complex Hadamard matrix arising from the master-function construction, and $F_N$ denotes the Fourier matrix of order $N$. A Dic tu…

Let $F_7$ be the Fourier matrix of order $7$, and let $P_7^q$ denote the displayed Petrescu family, with $q\in\mathbb T$. A regular complex Hadamard matrix is one whose row scalar…

Let $F_{S,p}$ denote the partial Fourier matrix associated to a subset $S\subset\mathbb Z_p$, where $p$ is prime. Truncation conjecture. There exists a constant $\varepsilon>0$ suc…

Maximal-family conjecture. The maximal affine family of complex Hadamard matrices stemming from the Fourier matrix $F_d$ in dimensions $d=2p$, where $p$ is prime, is given by Eqs.…

Rational-span conjecture. One has