An AZ-style identity and Bollobás deficiency

The powerful AZ identity is a sharpening of the famous LYM-inequality. More generally, Ahlswede and Zhang discovered a generalization in which the Bollobás inequality for two set families can be lifted to an identity. In this paper, we show another generalization of the AZ identity. The new identity...

Full description

Saved in:
Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 114; no. 8; pp. 1504 - 1514
Main Author Thu, Tran Dan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2007
Subjects
Antichain
AZ identity
Bollobás inequality
LYM
LYM
Antichain
Bollobás inequality
AZ identity
Online AccessGet full text

Cover

More Information
Summary:The powerful AZ identity is a sharpening of the famous LYM-inequality. More generally, Ahlswede and Zhang discovered a generalization in which the Bollobás inequality for two set families can be lifted to an identity. In this paper, we show another generalization of the AZ identity. The new identity implies an identity which characterizes the deficiency of the Bollobás inequality for an intersecting Sperner family. We also give some consequences relating to Helly families and LYM-style inequalities.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2007.03.005