8 problems

Let $C\in\mathbb{C}^{d\times d}$ be a scaling matrix of rank four. A principal $4$-minor is non-vanishing when the corresponding principal submatrix has nonzero determinant. Rank-f…

Let $C_1,C_2\in\mathbb{C}^{d\times d}$ be scaling matrices, with associated delta-matroids, and let $c_1,c_2$ be the corresponding scalings. Delta-matroid invariance conjecture. If…

Assume $\operatorname{char} K=2$, let $F$ be the fixed field of the involution on $K$ with $F\ne K$, and write $K=F[\omega]$ where $\omega^2+\omega+\beta=0$ for some $\beta\in F$ a…

Let $K$ be a valued field with an automorphic involution preserving the valuation. Let $A=B+C$, where $B\in K^{n\times n}$ is skew-Hermitian and $C\in K^{n\times n}$ is Hermitian o…

Canonical form conjecture. For each binary $\Delta$-matroid $D$, there is a sequence of handle slides taking $D$ to some $D_{i,j,k,l}$ where $i$ is the size of the ground set minus…

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 $\Gamma$…

A matroid stack delta-matroid is a delta-matroid whose proper set systems in its stack are matroids. It is sparse paving when every matroid in its stack is sparse paving, meaning t…

For each $n\geq 2$, let $\Gamma_n$ be the proportion defined in the paper for compatible pairs of labelled delta-matroids. The sequence $(\Gamma_n)_{n\geq 2}$ is decreasing and bou…