论文标题
熵加权等级功能
Entropic Weighted Rank Function
论文作者
论文摘要
众所周知，一组共同分布的随机变量上的熵函数是一个集合设置函数。但是，并非任何表格函数是此形式的。在本文中，我们考虑了一个子模具集函数的家族，称为矩形的加权等级函数，并研究其熵的必要或充分条件。我们证明，加权等级函数位于子模锥的边界上。对于特征2字段上代表的矩形，我们表明整数有价值的加权等级函数是熵的。我们得出了一个必要的条件，即恒定重量级别的函数是熵的，并表明对于图形矩阵的情况，这种情况确实足够了。由于这些功能概括了Matroid的等级，因此我们的发现概括了Abbe等的一些结果。 al。关于矩阵的等级函数的熵特性。
It is known that the entropy function over a set of jointly distributed random variables is a submodular set function. However, not any submodular function is of this form. In this paper, we consider a family of submodular set functions, called weighted rank functions of matroids, and study the necessary or sufficient conditions under which they are entropic. We prove that weighted rank functions are located on the boundary of the submodularity cone. For the representable matroids over a characteristic 2 field, we show that the integer valued weighted rank functions are entropic. We derive a necessary condition for constant weight rank functions to be entropic and show that for the case of graphic matroids, this condition is indeed sufficient. Since these functions generalize the rank of a matroid, our findings generalize some of the results of Abbe et. al. about entropic properties of the rank function of matroids.
