AN IDENTITY IN COMBINATORIAL EXTREMAL THEORY

被引：29

作者：

AHLSWEDE, R

ZHANG, Z

机构：

[1] Universität Bielefeld, Fakultät für Mathematik, 4800 Bielefeld 1

来源：

ADVANCES IN MATHEMATICS | 1990年 / 80卷 / 02期

关键词：

D O I：

10.1016/0001-8708(90)90023-G

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our main discovery is the following identity: For every family A ⊂ 2Ω of non-empty subsets of Ω = {1, 2, ..., n} ∑ X⊂ω WA(X) ∥X∥( n X)≡1 where WA(X)=| {n-ary intersection} X⊃Aε{lunate}AA|. It can be viewed as a sharpening of the famous LYM-inequality. We present also generalizations to other posets. The total impact for combinatorics remains to be explored. The identity seems to be particularly useful for uniqueness proofs in Sperner Theory. We also discuss a geometric consequence. © 1990.

引用

页码：137 / 151

页数：15

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