An AZ-style identity and Bollobás deficiency

Authors:
Tran Dan Thu
Affiliations:
Faculty of Information Technology, University of Natural Sciences, 227 Nguyen van Cu, Dist. 5, HoChiMinh City, Viet Nam
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 6
Cited 0

Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability

Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
An induction proof of the Ahlswede-Zhang identity

Journal of Combinatorial Theory Series A
The dual of the Ahlswede-Zhang identity

Journal of Combinatorial Theory Series A
Extremal cases of the Ahlswede-Cai inequality

Journal of Combinatorial Theory Series A
Incomparability and intersection properties of Boolean interval lattices and chain posets

European Journal of Combinatorics
Regular Article: Pseudo-LYM Inequalities and AZ Identities

Advances in Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The powerful AZ identity is a sharpening of the famous LYM-inequality. More generally, Ahlswede and Zhang discovered a generalization in which the Bollobas 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 Bollobas inequality for an intersecting Sperner family. We also give some consequences relating to Helly families and LYM-style inequalities.