Solution of an extremal problem for sets using resultants of polynomials

A. Blokhuis

doi:10.1007/BF02128673

Solution of an extremal problem for sets using resultants of polynomials

A. Blokhuis

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

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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 iBj¦=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.

Original language	English
Pages (from-to)	393-396
Number of pages	4
Journal	Combinatorica
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/BF02128673
Publication status	Published - 1990

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10.1007/BF02128673

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@article{918f33bda13145f6a264b9173693332a,

title = "Solution of an extremal problem for sets using resultants of polynomials",

abstract = "A new, short proof is given of the following theorem of Bollob{\'a}s: LetA 1,..., Ah andB 1,..., Bh be collections of sets with i ¦A i¦=r,¦Bi¦=s and ¦A iBj¦={\O} 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.",

author = "A. Blokhuis",

year = "1990",

doi = "10.1007/BF02128673",

language = "English",

volume = "10",

pages = "393--396",

journal = "Combinatorica",

issn = "0209-9683",

publisher = "Janos Bolyai Mathematical Society",

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T1 - Solution of an extremal problem for sets using resultants of polynomials

AU - Blokhuis, A.

PY - 1990

Y1 - 1990

N2 - 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 iBj¦=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.

AB - 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 iBj¦=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.

U2 - 10.1007/BF02128673

DO - 10.1007/BF02128673

M3 - Article

SN - 0209-9683

VL - 10

SP - 393

EP - 396

JO - Combinatorica

JF - Combinatorica

IS - 4

ER -

Solution of an extremal problem for sets using resultants of polynomials

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