5 problems

Let $\Gamma$ be a finite group and let $\mathcal{M}$ be a minor-closed class of matroids, each represented by a $\Gamma$-gainable biased framework, meaning a biased framework whose…

Let $\Gamma$ be a finite group and let $\mathcal{G}$ be a minor-closed class of $\Gamma$-gainable biased graphs. An excluded minor for $\mathcal{G}$ is a biased graph outside…

Let $\Gamma$ be a finite group. A $\Gamma$-gainable biased graph is a biased graph admitting a gain assignment over $\Gamma$, and an excluded minor for a class is a graph outside t…

Let $[n]=\{1,\ldots,n\}$, and let $\mathbf{B}_n$ be the set of simple biased graphs with vertex set $[n]$. Let $\mathbf{H}_n$ be the set of those graphs that are group-labellable,…

Let $\mathbb F$ be a field, let $M$ be a frame matroid or lifted graphic matroid, and let $A$ be an $\mathbb F$-representation of $M$. A canonical representation is a frame matrix…