solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看3649次
Discrete Entropy Power Inequalities via Sperner Theory. (arXiv:1712.00913v2 [math.CO] UPDATED)
来源于:arXiv
A ranked poset is called strongly Sperner if the size of $k$-family cannot
exceed the sum of $k$-largest Whitney numbers. In a sense of function ordering,
a function $f$ is (weakly) majorized by $g$ if the the sum of $k$-largest
values in $f$ cannot exceed the sum of $k$-largest values in $g$. Two
definitions arise from different contexts, but each share a strong similarity
with each other. Furthermore, the product of two weighted posets assumes a
structural similarity with a convolution of two functions. Elements in the
product of weighted posets with ranks capture underlying structures of the
building blocks in the convolution. Combining all together, we are able to
derive several types of entropy inequalities including discrete entropy power
inequalities, and discuss more applications. 查看全文>>