Medians are below joins in semimodular lattices of breadth 2

• Published in: arXiv.org
• Main Authors: Czédli, Gábor, Powers, Robert C, White, Jeremy M
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 05.11.2019
• Subjects: Lattice modules; Lattices; Theorems

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 to \(L\) is called a median of \(\xi\) if the sum \(d(y,x_1)+\cdots+d(y,x_k)\) is minimum. The lattice \(L\)...