论文标题
整数分区的Gini索引
The Gini Index of an Integer Partition
论文作者
论文摘要
Gini指数是一个试图衡量资源在整个人群中分配的数字，并且通常在经济学中用作衡量财富或收入不平等的衡量。 Gini指数通常定义为分布的Lorenz曲线与平等线之间的面积，将其归一化为零和一个之间。以这种方式，我们在整个整数分区上定义了一个Gini索引，并表明它与第二个基本对称多项式和分区的优势顺序密切相关。我们以GINI指数的生成函数结束，并讨论如何使用它来在优势晶格的宽度上找到下限。
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.
