The dual of the ahlswede-zhang identity

Daykin, D. E.; Thu, Tran Dan

doi:10.1016/0097-3165(94)90105-8

Cited by 6 publications

(2 citation statements)

References 2 publications

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“…In the same way as in [10], we can obtain the dual identity of (T1) which can be presented in the following theorem. We notice that the above dual identity does not contain a term depending on n. From this identity, we can get another formula of the Bollobás deficiency (also the deficiency of Tuza identity in Theorem 4) as follows (put q = n − 1, B = cA):…”

Section: Notesmentioning

confidence: 93%

An AZ-style identity and Bollobás deficiency

Thu

2007

Journal of Combinatorial Theory, Series A

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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.

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Section: Notesmentioning

confidence: 93%

An AZ-style identity and Bollobás deficiency

Thu

2007

Journal of Combinatorial Theory, Series A

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“…Moreover, the generalisation of the AZ identity [2] implies Bollobás inequality for two set systems [7]. Several results on AZ-style identities are also proposed; for example, AZ-style identities for other posets [3], pseudo-LYM inequalities and AZ identities [11], duals of AZ-identities [9,12], AZ type identity for k-chains in k-Sperner families [14], extremal cases of the Ahlswede-Cai identity [15], parametrised AZ identity [17].…”

Section: Introductionmentioning

confidence: 99%

On Half-Way AZ-Style Identities

Thu

2011

Graphs and Combinatorics

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The Ahlswede-Zhang identity is an elegant sharpening of the famous LYM-inequality. Recently, we have found a parametrised identity which implies the AZ identity and characterizes deficiencies of other inequalities in combinatorics. In this paper, we show identities of half-way extraction from AZ-style identities. These identities aim to characterize more clearly terms participating in AZ identities or LYM-style inequalities.

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On Local LYM Identities

Thu

2013

Ann. Comb.

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The dual of the ahlswede-zhang identity

Cited by 6 publications

References 2 publications

An AZ-style identity and Bollobás deficiency

An AZ-style identity and Bollobás deficiency

On Half-Way AZ-Style Identities

On Local LYM Identities

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