MathOverflow

Reutenauer & Straubing (1984) showed that all commutative semirings are stably finite, and Yi-Jia Tan (2016) showed that nontrivial commutative semirings satisfy the strong rank condition (Theorem 3.2) building on the work. The Orzech property for...

Let $a>0$. Is there $\varepsilon>0$ such that, for all finite groups $G$ and all subsets $A\subseteq G$ with $|A|\geq a|G|$, we have $\frac{1}{|G|}\sum_{g\in G}|A\cap g^2A|\geq\varepsilon|G|$?
Remark: In abelian groups you can always take $\varepsilon=a^2$. This is because abelian groups $G$ act on themselves by $\mu$-preserving (where $\mu$ is normalized counting measure in $G$) actions $T_g:G\to G;x\mapsto g^2x$, for $g\in G$, and using...

Strassen has defined a partial order on nilpotent quiver representations over $\mathbb C$ called asymptotic degeneration. I was wondering whether it can be generalized to an arbitrary field $k$? It didn't seem to me have to be on $\mathbb C$. The link...

I am currently working on the formalization of representation-theoretic multiplicity obstructions within the Geometric Complexity Theory (GCT) framework, specifically focusing on the separation of the padded permanent from the orbit closure of the determinant...