Zoltán Füredi Explained

Zoltán Füredi (Budapest, Hungary, 21 May 1954) is a 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 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.

Some results

In infinitely many cases he determined the maximum number of edges in a graph with no C₄.^[1]
With Paul Erdős he proved that for some c>1, there are c^d points in d-dimensional space such that all triangles formed from those points are 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^d.
He proved that there are at most

O(nlogn)

unit distances in a convex n-gon.^[2]

In a paper written with coauthors he solved the Hungarian lottery problem.^[3]
With Ilona Palásti he found the best known lower bounds on the orchard-planting problem of finding sets of points with many 3-point lines.^[4]
He proved an upper bound on the ratio between the fractional matching number and the matching number in a hypergraph.^[5]

Füredi . Zoltán . Graphs without quadrilaterals . Journal of Combinatorial Theory, Series B . Elsevier BV . 34 . 2 . 1983 . 0095-8956 . 10.1016/0095-8956(83)90018-7 . 187–190. free .
Z. Füredi. The maximum number of unit distances in a convex n-gon. Journal of Combinatorial Theory. Series A. 55. 2. 1990. 316–320. 10.1016/0097-3165(90)90074-7. free.
Z. Füredi, G. J. Székely, and Z. Zubor. On the lottery problem. Journal of Combinatorial Designs. 4. 1. 1996. 5–10. 10.1002/(sici)1520-6610(1996)4:1<5::aid-jcd2>3.3.co;2-w. http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1520-6610(1996)4:1%3C5::AID-JCD2%3E3.0.CO;2-J/abstract Reprint
Arrangements of lines with a large number of triangles. Füredi. Palásti. Z.. I.. Proceedings of the American Mathematical Society. 92. 4. 561–566. 1984. 2045427. 10.1090/S0002-9939-1984-0760946-2. free. .
Füredi. Zoltán. 1981-06-01. Maximum degree and fractional matchings in uniform hypergraphs. Combinatorica. 1. 2. 155–162. 10.1007/BF02579271. 10530732. 1439-6912.