8 problems

Let $\mathcal B_f^{(x)}$ be a Brauer algebra with parameter $x$, and consider the generic indecomposable $\mathcal B_f^{(x)}$-modules and the standard filtration of the algebra. Th…

For nonzero integers $a,b,c$ with $a+b=c$, the ABC consequence. For each $\varepsilon>0$, there exists a constant $K_\varepsilon$ such that … This is stated as a folklore consequen…

Let $k$ and $\ell$ be integers greater than $1$, and let $m$ and $n$ be integers. Define … where $\operatorname{rad}(r)$ is the largest squarefree divisor of $r$. Finiteness conjec…

Woods's conjecture. If $k$ is sufficiently large, then this sequence uniquely determines $n$. This is a stronger form of Erdős's bounded radical-sequence conjecture; the source giv…

Let $m$ and $n$ be integers, and let $\operatorname{rad}(r)$ denote the largest squarefree divisor of an integer $r$. Erdős's conjecture. There is a fixed constant $K$ such that fo…

Define … Radical characterization conjecture. One has … The surrounding results show that $\overline{\mathcal{R}}$ is finite and constrain its elements; the conjecture remains unre…

Let $V$ be a vector space and let $\mathcal L$ be a series in $V$. Define … where $S(\mathcal L)$ is the stabilizer of $\mathcal L$, and let $H(\mathcal L)$ denote the Hirsch–Plotk…

Let $V$ be an $\mathbb F$-vector space, let $\mathcal L$ be a series in $V$, and let $H(\mathcal L)$ be the Hirsch–Plotkin radical of $S(\mathcal L)$, the stability group of…