3 problems

Let $M$ be a matroid on a ground set $E$, let $\Gamma$ be an abelian group, let $\psi\colon E\to\Gamma$ be a group labeling, let $F\subseteq\Gamma$ be a finite set, and let…

Let $\Gamma$ be a finite abelian group. Its Davenport constant $D(\Gamma)$ is the least positive integer such that every sequence of $D(\Gamma)$ elements of $\Gamma$ has a nonempty…

Let $M$ be a matroid with ground set $E$, let $\Gamma$ be an abelian group, let $\psi\colon E\to\Gamma$ be a group labeling, and let $F\subseteq\Gamma$ be a finite set of forbidden…