Journal of Integer Sequences, Vol. 23 (2020), Article 20.9.7

The Gini Index of an Integer Partition

Grant Kopitzke
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.

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(Concerned with sequences A076269 A337206.)

Received June 15 2020; revised version received August 19 2020. Published in Journal of Integer Sequences, October 16 2020.

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