Sums of finite subsets in Rd

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.012

Mario Huicochea

引用次数: 2

Abstract

Let $B_{1}, B_{2}, \dots, B_{m}$ be nonempty finite subsets of $R^{d}$ with $B_{i}$ not contained in an affine hyperplane for each $i \in {2, 3, \dots, m}$ . First we get a sharp lower bound on $| B_{1} + B_{2} |$ when $| B_{2} | = d + 1$ . Using this result and other ideas, we find a nontrivial lower bound on $| B_{1} + B_{2} + \dots + B_{m} |$ which generalizes a result of M. Matolcsi and I. Z. Ruzsa [7].

查看原文本刊更多论文

Rd中有限子集的和

设B1,B2，…，Bm是Rd的非空有限子集，且对于每个i∈{2,3，…，m}， Bi不包含在仿射超平面上。首先，当|B2|=d+1时，我们得到了一个明显的下界。利用这一结果和其他思想，我们得到了一个非平凡下界，推广了M. Matolcsi和I. Z. Ruzsa[7]的结果。

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.