6 problems

Let $\mathbb{P}=(R,G)$ be a skew partial field, and let $M$ be a matroid that is $\mathbb{P}$-representable, meaning that it arises from a $\mathbb{P}$-chain group as in the source…

Let $G$ be an abelian group, and let a Dowling geometry be the matroid constructed from the corresponding labelled graph whose circuits are the positive cycles and minimal connecte…

Let $\mathcal{K}_\infty$ denote the class obtained from the hierarchy of Kinser classes, and let $\mathcal{K}_\infty^*$ denote its dual class. Infinite Kinser class self-duality co…

For each integer $n>4$, let $\mathcal{K}_n$ be the class of matroids satisfying the $n$-th Kinser inequality, and let $\mathcal{K}_n^*$ denote its dual class. Kinser hierarchy dual…

For an integer $n>5$, let ${\mathrm{Kin}(n)}^-$ denote the matroid referred to in the source as ${\mathrm{Kin}(n)}^-$. Let $\mathcal{K}_n$ be the class of matroids satisfying the…

For each integer $n>5$, let $\mathcal{K}_n$ be the class of matroids satisfying the $n$-th Kinser inequality, and let $\mathcal{K}_n^*$ denote its dual class. Kinser class non-dual…