Combinatorica

, Volume 10, Issue 4, pp 393–396 | Cite as

Solution of an extremal problem for sets using resultants of polynomials

  • A. Blokhuis
Note

Abstract

A new, short proof is given of the following theorem of Bollobás: LetA1,..., Ah andB1,..., Bh be collections of sets with ∀ i ∶¦Ai¦=r,¦Bi¦=s and ¦Ai∩Bj¦=Ø if and only ifi=j, thenh≤( s r+s ). The proof immediately extends to the generalizations of this theorem obtained by Frankl, Alon and others.

AMS subject classification (1980)

05 C 65 

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References

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    N. Alon: An Extremal Problem for Sets with Applications to Graph Theory,Journal of Combinatorial Theory, Series A,40 (1985), pp. 82–89.Google Scholar
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    L.Babai, and P.Frankl:Linear algebra methods in combinatorics, part 1, Department of Computer Science of the University of Chicago,1988.Google Scholar
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    B. Bollobás: On generalized graphs,Acta Math. Acad. Sci. Hungar.,16 (1965), pp. 447–452.CrossRefGoogle Scholar
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    G. Kalai: Intersection patterns of convex sets,Israel J. Math.,48 (1984), 161–174.Google Scholar
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    L. Rédei:Algebra, Volume 1, Pergamon Press, Oxford,1967.Google Scholar
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    B. L. van der Waerden:Algebra Erster Teil, Springer Verlag, Berlin Heidelberg New York,1966.Google Scholar

Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • A. Blokhuis
    • 1
  1. 1.Dept. of Mathematics and Comp. Sci.Eindhoven University of TechnologyMB, EindhovenThe Netherlands

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