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'''Zoltán Füredi''' ([[Budapest]], [[Hungary]], 21 May 1954) is a [[Hungarian people|Hungarian]] mathematician, working in [[combinatorics]], mainly in [[discrete geometry]] and extremal combinatorics. He was a student of [[Gyula O. H. Katona]]. He is a corresponding member of the [[Hungarian Academy of Sciences]] (2004). He is a research professor of the [[Alfréd Rényi Institute of Mathematics|Rényi Mathematical Institute]] of the Hungarian Academy of Sciences, and a professor at the [[University of Illinois Urbana-Champaign]] (UIUC).


Füredi received his [[Candidate of Sciences]] degree in mathematics in 1981 from the Hungarian Academy of Sciences.<ref>{{MathGenealogy|id=24920}}</ref>
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==Some results==
* In infinitely many cases he determined the maximum number of edges in a [[graph (mathematics)|graph]] with no [[cycle graph|''C''<sub>4</sub>]].
* With [[Paul Erdős]] he proved that for some ''c''>1, there are ''c''<sup>''d''</sup> points in ''d''-dimensional space such that all triangles formed from those points are [[triangle#By internal angles|acute]].
* With [[Imre Bárány]] he proved that no [[polynomial time]] algorithm determines the volume of [[convex bodies]] in dimension ''d'' within a multiplicative error ''d''<sup>''d''</sup>.
* He proved that there are at most <math>O(n\log n)</math> unit distances in a convex n-gon.<ref>{{Cite journal|author=Z. Füredi|title=The maximum number of unit distances in a convex n-gon|journal=Journal of Combinatorial Theory|volume=55|issue=2|year=1990|pages=316–320|doi=10.1016/0097-3165(90)90074-7}}</ref>
* In a paper written with coauthors he solved the Hungarian [[lottery]] problem.<ref>{{Cite journal|author=Z. Füredi, [[Gabor Szekely|G. J. Székely]], and Z. Zubor|title=On the lottery problem|journal=Journal of Combinatorial Designs|volume=4|issue=1|year=1996|pages=5–10|publisher=Wiley}} [http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1520-6610(1996)4:1%3C5::AID-JCD2%3E3.0.CO;2-J/abstract] [http://www.math.uiuc.edu/~z-furedi/PUBS/furedi_lotto.pdf Reprint]</ref>
* With I. Palásti he found the best known lower bounds on the [[orchard-planting problem]] of finding sets of points with many 3-point lines.<ref>{{citation|title=Arrangements of lines with a large number of triangles|last1=Füredi|last2=Palásti|first1=Z.|first2=I.|journal=Proceedings of the American Mathematical Society|volume=92|issue=4|pages=561–566|year=1984|url=http://www.jstor.org/stable/2045427}}.</ref>
 
==References==
<references/>
 
==External links==
* [http://www.math.uiuc.edu/~z-furedi/ Füredi's UIUC home page]
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              =Furedi, Zoltan
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Hungarian mathematician
| DATE OF BIRTH    = 21 May 1954
| PLACE OF BIRTH    =
| DATE OF DEATH    =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Furedi, Zoltan}}
[[Category:Hungarian mathematicians]]
[[Category:Members of the Hungarian Academy of Sciences]]
[[Category:Combinatorialists]]
[[Category:University of Illinois at Urbana–Champaign faculty]]
[[Category:1954 births]]
[[Category:Living people]]
 
 
{{Hungary-scientist-stub}}
{{Europe-mathematician-stub}}

Revision as of 04:25, 18 February 2014

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