Bivariate Bonferroni-type inequalities based on multivariate Lagrange interpolation

Gergely Mádi-Nagy; András Prékopa

doi:10.1556/sscmath.52.2015.1.1299

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 52: Issue 1

Bivariate Bonferroni-type inequalities based on multivariate Lagrange interpolation

Authors:

Gergely Mádi-Nagy

Gergely Mádi-Nagy Eötvös University Department of Operations Research Pázmány Péter sétány 1/c Budapest H-1117 Hungary

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András Prékopa

András Prékopa

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Pages:: 21–39

Online Publication Date:: 17 Mar 2015

Publication Date:: 01 Mar 2015

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.52.2015.1.1299

Keywords:: Primary 60E15; 62E99; 65D05; Bonferroni-type inequalities; multivariate Lagrange interpolation

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Let A₁,...,A_N and B₁,...,B_M be two sequences of events and let ν_N(A) and ν_M(B) be the number of those A_i and B_j, respectively, that occur. Based on multivariate Lagrange interpolation, we give a method that yields linear bounds in terms of S_k,t, k+t ≤ m on the distribution of the vector (ν_N(A), ν_M(B)). For the same value of m, several inequalities can be generated and all of them are best bounds for some values of S_k,t. Known bivariate Bonferroni-type inequalities are reconstructed and new inequalities are generated, too.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Gábor SÁGI (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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