5 problems

A gross substitute valuation is a valuation arising in the gross-substitutes framework, and a weighted matroid rank function is a function obtained by assigning nonnegative weights…

Let $\omega\colon \binom{E}{r}\to\mathbb{R}\cup\{-\infty\}$ be a valuated matroid of rank $r$ on a ground set $E$. The source's preceding discussion defines the desired exchange pr…

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…

A weighted matroid rank function is obtained from a matroid by assigning nonnegative weights to its elements and maximizing the total weight of an independent subset contained in a…