10 problems

Let $M$ be a dyadic matroid, meaning a matroid representable over the dyadic partial field. Let $P(M)$ be its matroid base polytope. Dyadic matroid triangulation conjecture. The ma…

Let $\mathbb{P}$ be a partial field, and let $\mathbb{L}\mathbb{P}$ denote its lift, constructed from the fundamental elements of $\mathbb{P}$. Pendavingh's idempotence conjecture.…

Let $\Gamma$ be a finite abelian group of order at least $2$, and let $\mathbb{F}$ be a finite field. A $\Gamma$-graphic delta-matroid is a delta-matroid associated with a $\Gamma$…

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

A matroid is linear if it is representable by a vector configuration over a field, and algebraic if it is algebraic over a field. Almost-all non-representability conjecture. Almost…

Let $\mathbb{G}$ denote the golden-ratio partial field. Golden-ratio partial-field conjecture. A matroid is representable over $\operatorname{GF}(4)\otimes\mathbb{R}$ if and only i…

Uniform partial-field characterization conjecture. A matroid is representable over $\operatorname{GF}(2^k)$ for all $k>1$ if and only if it is representable over…

Let $\mathbb{P}$ be a partial field, and let $\mathbb{L}\mathbb{P}$ denote its lift. Lift idempotence conjecture. … The conjecture is related to whether the canonical homomorphism…

$\mathbb{P}_4$ characterization conjecture. A matroid $M$ is representable over all finite fields with at least $4$ elements if and only if $M$ is representable over $\mathbb{P}_4$…

Let $k$ be a prime power. The claim concerns matroids and representability over fields and finite fields $\operatorname{GF}(q)$. Finite-field list conjecture. There exists a number…