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arXiv · 2005.04284

The Gini Index of an Integer Partition

Grant Kopitzke
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Abstract

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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Grant Kopitzke. 2020-05-08. The Gini Index of an Integer Partition. https://arxiv.org/abs/2005.04284

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