Lattices of partial sums

Abstract

In this paper we introduce and study a class of partially ordered sets that can be interpreted as partial sums of indeterminate real numbers. An important example of these partially ordered sets, is the classical Young lattice \(\mathbb{Y}\) of the integer partitions. In this context, the sum function associated to a specific assignment of real values to the indeterminate variables becomes a valuation on a distributive lattice.