11 problems

Let $ll,t in N$ with $ll ge 3$, and let $\falM$ be the class of $R$-representable matroids with no $U_{2,ll+2}$-minor and no $M(K_t)$-minor. Here $alpha$ is the constant appearing…

Let $M$ be a representable matroid with set of circuits $\mathcal{C}$. For matroids on a fixed ground set, use the weak order defined by $M_1\geq M_2$ when every dependent set of…

Let $R\in\mathbb{Z}^{k\times n}$ be sufficiently generic, so that $M(R)=U(k,n)$, and let $\delta_{OW}M(R)$ denote the Oxley–Wang derived matroid of the representation $R$. Generici…

Let ${\mathbb K}$ be an infinite field, and let the class of ${\mathbb K}$-representable matroids be the minor-closed class consisting of matroids representable over ${\mathbb K}$.…

Let $q$ be an integer at least two, let $p_q$ be the largest prime less than or equal to $q$, and let $M$ be a simple matroid of rank $r$ with no $U_{2,2+q}$-minor. The known bound…

The asymptotic enumeration conjecture. Asymptotically almost all representable matroids on $[n]$ have rank in $\{\lfloor n/2\rfloor,\lceil n/2\rceil\}$ and exactly $d(n)-1$ nonbase…

Let $N$ be a real-representable matroid. An excluded minor for the class of real-representable matroids is a matroid that is not real-representable while all of its proper minors a…

A representable matroid is a matroid satisfying the rank axioms of a matroid and representable over a field. Mayhew–Newman–Whittle conjecture. It is impossible to characterise the…

For a matroid $M$ on ground set $E(M)$, let $Q,R,S,T\subseteq E(M)$ satisfy $Q\cap R=S\cap T=\emptyset$. Write … Let $c:\mathbb{N}^2\to\mathbb{N}$ be a function. Geelen's conjectur…

Let $N$ be a $\operatorname{GF}(q)$-representable matroid, and let $\operatorname{bw}(M)$ denote the branch width of a matroid $M$. High-branch-width non-fragility conjecture. Ther…

Fix a matroid $N$. A matroid $M$ is $N$-fragile if, for every $e\in E(M)$, at least one of $M{-} e$ and $M/e$ has no $N$-minor. Bounded Canopy Conjecture. For every prime power $q$…