Medians are below joins in semimodular lattices of breadth 2

Gábor Czédli, Robert C. Powers, Jeremy M. White

Let $L$ be a lattice of finite length and let $d$ denote the minimum path length metric on the covering graph of $L$. For any $\xi =(x_1,\dots ,x_k)\in L^k$, an element $y$ belonging t…