On the discrete Brunn-Minkowski inequality by Gradner&Gronchi

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.051

David Iglesias

引用次数: 0

Abstract

In 2002 Gardner and Gronchi obtained a discrete analogue of the Brunn-Minkowski inequality. They proved that for finite subsets $A, B \subset R^{n}$ with $\dim B = n$ , the inequality $| A + B | \geq | D_{| A |}^{B} + D_{| B |}^{B} |$ holds, where $D_{| A |}^{B}, D_{| B |}^{B}$ are particular subsets of the integer lattice, called B-initial segments. The aim of this paper is to provide a method in order to compute $| D_{| A |}^{B} + D_{| B |}^{B} |$ and so, to implement this inequality.

查看原文本刊更多论文

关于离散Brunn-Minkowski不等式的Gradner&Gronchi

2002年，Gardner和Gronchi获得了Brunn-Minkowski不等式的离散模拟。他们证明了对于dim (B) =n的有限子集A,B∧Rn，不等式|A+B|≥|D|A|B+D|B|B|成立，其中D|A|B,D|B|B是整数格的特定子集，称为B初始段。本文的目的是提供一种计算|D| a |B+D|B|B|等的方法来实现这个不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.