关于离散Brunn-Minkowski不等式的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

摘要

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。

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On the discrete Brunn-Minkowski inequality by Gradner&Gronchi

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.

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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

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