Vietnam Journal of Mathematics

, Volume 43, Issue 4, pp 771–775 | Cite as

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

  • Tran Thai-Duong
  • Tran Dan ThuEmail author


This paper gives a simple proof for a generalized form of the AZ-identity of one or two set systems. We also extend the results further and establish some new identities related to the AZ-identity. Our method uses some properties of rational functions.


Antichain Upset Downset AZ identity LYM inequality 

Mathematics Subject Classification (2010)




The author wishes to thank anonymous referees for their valuable suggestions to improve the paper. The paper is supported by Vietnam National University, Ho Chi Minh City; Project No. HS2014-18-03.


  1. 1.
    Ahlswede, R., Zhang, Z.: An identity in combinatorial extremal theory. Adv. Math. 80, 137–151 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Ahlswede, R., Cai, N.: A generalisation of the AZ identity. Combinatorics 13, 241–247 (1993)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Daykin, D.E., Tran, D.T.: The dual of Ahlswede–Zhang identity. J. Comb. Theory Ser. A 68, 246–249 (1994)zbMATHCrossRefGoogle Scholar
  4. 4.
    Ku, C.Y., Wong, K.B.: On AZ-style identity. arXiv:1107.1296 (2011)
  5. 5.
    Tran, D.T.: An AZ-style identity and Bollobás deficiency. J. Comb. Theory Ser. A 114, 1504–1514 (2007)zbMATHCrossRefGoogle Scholar

Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.International University, National University Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.University of Science, National University Ho Chi Minh CityHo Chi Minh CityVietnam

Personalised recommendations