2 problems

Let $\mathbb{P}_2(n)$ denote the lattice of subspaces of an $n$-dimensional vector space over $\mathbb{F}_2$. A subset $\mathcal{U} \subseteq \mathbb{P}_2(n)$ is a linear code if i…

Let $L$ be a finite geometric lattice, and let its Whitney numbers of the second kind be the numbers counting elements of each rank. Welsh's conjecture. The Whitney numbers of the…