Solution of an extremal problem for sets using resultants of polynomials

Abstract

A new, short proof is given of the following theorem of Bollobás: LetA 1,..., Ah andB 1,..., Bh be collections of sets with ∀ i ∶¦A i¦=r,¦Bi¦=s and ¦A i∩Bj¦=Ø if and only ifi=j, thenh≤( r+ss ). The proof immediately extends to the generalizations of this theorem obtained by Frankl, Alon and others.

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Blokhuis, A. Solution of an extremal problem for sets using resultants of polynomials. Combinatorica 10, 393–396 (1990). https://doi.org/10.1007/BF02128673

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AMS subject classification (1980)

  • 05 C 65