The Gini Index of an Integer Partition
Department of Mathematics
University of Wisconsin, Milwaukee
Milwaukee, WI 53211
The Gini index is a number that attempts to measure how equitably a
resource is distributed throughout a population, and is commonly used
in economics as a measurement of inequality of wealth or income. The
Gini index is often defined as the area between the Lorenz curve of a
distribution and the line of equality, normalized to be between zero
and one. In this fashion, we define a Gini index on the set of integer
partitions and show that it is closely related to the second elementary
symmetric polynomial, and the dominance order on partitions. We conclude
with a generating function for the Gini index, and discuss how it can
be used to find lower bounds on the width of the dominance lattice.
Full version: pdf,
(Concerned with sequences
Received June 15 2020;
revised version received August 19 2020.
Published in Journal of Integer Sequences,
October 16 2020.
Journal of Integer Sequences home page