Bounds on maximal families of sets not containing three sets with A ∧ B ⊂ C, A ⊄ B

被引：17

作者：

Carroll, Teena ^{[2
]}

Katona, Gyula O. H. ^{[1
]}

机构：

[1] Renyi Inst, Budapest, Hungary

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2008年 / 25卷 / 03期

关键词：

extremal problem for families; sperner type theorem; forbidden subposet;

D O I：

10.1007/s11083-008-9090-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Lower and upper estimates are given on the size of a family of subsets of an n- element set containing no three distinct sets satisfying A boolean AND B subset of C, A not subset of B. This is a sharpening of an earlier result where the same question was solved under the condition that there are no three distinct sets such that A boolean AND B subset of C.

引用

页码：229 / 236

页数：8

共 9 条

[1]

Alon N., 2004, The probabilistic method

[2] Largest families without an r-Fork [J].