Jiaqi Liao

Erd\H{o}s--Ko--Rado and Hilton--Milner Theorems in the Partition Lattice

Let $M_n=M(K_{n+1})$ be the graphic matroid of the complete graph, and let $\mathcal{F}_k(M_n)$ be its rank-$k$ flats. We study families $\mathcal{A}\subseteq\mathcal{F}_k(M_n)$ satisfying $\mathrm{rk}(A\wedge B)\ge t$ for all $A,B\in\mathcal{A}$. For $t=1$, this problem is exactly equivalent to Czabarka's partition-EK...