6 problems

Strict inclusion conjecture. In each of these two cases, the class of multilinear matroids is strictly contained in the corresponding broader class.

Let $\mathbb{P}=(R,G)$ be a skew partial field, let $n,r,s$ be positive integers with $s\geq r$, define … and let $A$ be an $X\times E$ weak $\mathbb{P}$-matrix. A map…

Let $\mathbb{H}$ be the quaternions, with norm $|\cdot|$, and let $p,q,r\in\mathbb{H}$ satisfy … for all distinct $i,j\in\{0,1,p,q,r\}$. Let $M$ be a quaternionic unimodular matroi…

Let $\mathbb{P}$ be a skew partial field, and let $M_1$ and $M_2$ be $\mathbb{P}$-representable matroids having a common flat $N$ and representations that agree on $N$. If $N$ is a…

Let $M$ be a matroid representable over a skew partial field, and let a quadruple of subsets of $M$ be given. Ingleton inequality conjecture. Ingleton's Inequality is satisfied by…

A skew partial field is a partial field whose multiplicative group need not be commutative. Let $\mathbb{P}(n,\mathbb{F})$ denote the partial field associated with $n\times n$ matr…