Forbidden (0,1)-vectors in Hyperplanes of R~n: The unrestricted case

R. AHLSWEDE; H. AYDINIAN; L. H. KHACHATRIAN

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Forbidden (0,1)-vectors in Hyperplanes of R~n: The unrestricted case

机译：R〜n的超平面中的禁止（0,1）-向量：无限制情况

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In this paper, we continue our investigation on "Extremal problems under dimension constraints" introduced. The general problem we deal with in this paper can be formulated as follows. Let U be an affine plane of dimension k in R~n. Given F is contained in E(n) = {0, 1}~n is contained in R~n determine or estimate max {|U∩E(n)|:U∩F = Φ}. Here we consider and solve the problem in the special case where U is a hyperplane in R~n and the "forbidden set" F = E(n, k) = {x~n ∈ E(n):x~n has k ones}. The same problem is considered for the case, where U is a hyperplane passing through the origin, which surprisingly turns out to be more difficult. For this case we have only partial results.

机译：在本文中，我们将继续对引入的“尺寸约束下的极端问题”进行研究。我们在本文中处理的一般问题可以表述如下。设U为R〜n中尺寸为k的仿射平面。给定F包含在E（n）= {0，1}〜n中包含在R〜n中，确定或估计最大值{|U∩E（n）|：U∩F=Φ}。在这里，我们考虑并解决特殊情况下的问题，在这种特殊情况下，U是R〜n中的一个超平面，“禁集” F = E（n，k）= {x〜n∈E（n）：x〜n有k那些}。对于U是穿过原点的超平面的情况，也考虑了相同的问题，令人惊讶地发现这更加困难。对于这种情况，我们只有部分结果。

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来源
《Designs, Codes and Crytography》 |2005年第1期|p.151-167|共17页
作者
R. AHLSWEDE; H. AYDINIAN; L. H. KHACHATRIAN;
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作者单位

Fakultaet fuer Mathematik, Universitaet Bielefeld, Universitaetsttr. 25, 33615 Bielefeld, Germany;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
combinatorial extremal theory; (0,1)-vectors; dimension constraints; forbidden weights;

机译：组合极值理论;（0,1）-向量;尺寸约束;禁止权重;

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Forbidden (0,1)-vectors in Hyperplanes of R~n: The unrestricted case

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