4 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…

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…

A valuation $v:2^{\mathcal G}\to\mathbb R_+$ assigns a value to each bundle of items, and a gross substitutes valuation is a valuation in the gross substitutes class. A Rado valuat…

Matroid-based valuation conjecture. For each $n\geq 1$ and every $v\in\mathcal{GSV}_n$, there exists an integer $m(n)$ such that