5 problems

A Butson Hadamard matrix $BH(n,q)$ is an $n\times n$ complex matrix whose entries are $q$th roots of unity and whose rows are pairwise orthogonal under the standard complex inner p…

Let $H$ be a Butson-type matrix, let $k$ be an integer for which the $k$-th exterior product $\wedge^k H$ is defined, and let a generalised weighing matrix mean a matrix satisfying…

Let $p$ be a prime and let $t\geq 1$. A Butson-type Hadamard matrix $\operatorname{BH}(n,q)$ is a matrix of order $n$ whose entries are $q$-th roots of unity and whose rows are pai…

Egan–Ó Catháin conjecture. Is it true that

Let $n$ and $h$ be positive integers. A Butson Hadamard matrix of type $(\mathbb{Z}_n,h)$, denoted $\operatorname{BH}(\mathbb{Z}_n,h)$, is a group-invariant Hadamard matrix of orde…