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].

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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。

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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%

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