scholarly journals A generalization of the AZ identity

COMBINATORICA ◽  
1993 ◽  
Vol 13 (3) ◽  
pp. 241-247 ◽  
Author(s):  
Rudolf Ahlswede ◽  
Ning Cai
Keyword(s):  
Az Identity

A Simple Proof for a More Generalized Form of the AZ-identity

2015 ◽  
Vol 43 (4) ◽  
pp. 771-775 ◽  
Author(s):  
Tran Thai-Duong ◽  
Tran Dan Thu
Keyword(s):  
Simple Proof ◽  
Az Identity

AZ-style identities of downsets and upsets

2014 ◽  
Vol 06 (03) ◽  
pp. 1450040 ◽  
Author(s):  
Tran Dan Thu
Keyword(s):  
Set Function ◽  
Lym Inequality ◽  
Az Identity

The Ahlswede–Zhang identity is a sharpening of the well-known LYM inequality. To establish the identity, Ahlswede and Zhang introduced an important set function called AZ function. In this paper, we present some identities which establish a relation between the AZ function and cardinalities of downsets or upsets. Some connections of these identities with the original AZ identity are considered. Furthermore, these identities yield formulas concerning the size of a star in a downset.

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