Discrete Dynamics by Different Concepts of Majorization

Figure 4

(Left) Two Ruch lattices to show the order of discrete majorization. The arrows show the direction from the least upper bound to the greatest lower bound and characterize the discrete classical majorization. The dashed arrows between both lattices describe the weak submajorization [17]. The diagrams 𝑏 and 𝑐 characterize incomparableness in terms of classical majorization and the diagrams 𝑑 and 𝑥 incomparableness of the weak submajorization. (Right) The same Ruch lattices, but the dashed arrows represent the weak supermajorization.