Majorization of Finite Partially Ordered Sets
Ko‐Wei Lih · SIAM Journal on Algebraic and Discrete Methods · 1982
The classical concept of majorization between two finite sequences of real numbers is extended to between real-valued functions defined on a finite partially ordered set. We establish characterizations of majorization. The FKG and Holley inequalities from statistical mechanics have their majorization interpretations. Their validity is closely tied to the distributiveness of the background lattice. An equivalence proof is hence provided. Finally, suitable restrictions on the rearrangement of function values enable us to generalize the classical theorem of Schur–Ostrowski which characterizes functions preserving majorization in terms of relative orders of their first partial derivatives.