A generalization of the AZ identity

Abstract

The identity discovered in [1] can be viewed as a sharpening of the LYM inequality ([3], [4], [5]). It was extended in [2] so that it covers also Bollobás' inequality [6]. Here we present a further generalization and demonstrate that it shares with its predecessors the usefullness for uniqueness proofs in extremal set theory.

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Ahlswede, R., Cai, N. A generalization of the AZ identity. Combinatorica 13, 241–247 (1993). https://doi.org/10.1007/BF01202350

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AMS subject classification code (1991)

  • 05 A 19
  • 04 A 20