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# Kazimierz Zarankiewicz

Kazimierz Zarankiewicz (2 May 1902 – 5 September 1959) was a Polish mathematician. He was born in Częstochowa and died in London, England.

His main interest was topology. He studied at the University of Warsaw, together with Zygmunt Janiszewski, Stefan Mazurkiewicz, Wacław Sierpiński, Kazimierz Kuratowski, and Stanisław Saks. He wrote works on cut-points in connected spaces, on conformal mappings, on complex functions and number theory, and triangular numbers.

During World War II, Zarankiewicz took part in illegal teaching, forbidden by the German authorities, and eventually was sent to a concentration camp. He successfully survived and became a teacher at Warsaw University of Technology.

He visited universities in Tomsk, Harvard, London, Vienna. He served as president of the Warsaw section of the Polish Mathematical Society and the International Astronautical Federation.

The Zarankiewicz problem is named after Zarankiewicz; this problem asks, for a given size of (0,1)-matrix, how many matrix entries must be set equal to 1 in order to ensure that some a × b submatrix is made up only of 1's.

Also the Zarankiewicz Crossing Number Conjecture in the mathematical field of graph theory is named after Zarankiewicz. The conjecture states that the crossing number of a complete bipartite graph K_{m,n} equals

cr(K_{m,n}) = \lfloor n/2\rfloor\lfloor (n-1)/2\rfloor\lfloor m/2\rfloor\lfloor (m-1)/2\rfloor.\

Zarankiewicz proved that this formula is an upper bound for the actual crossing number. The problem of determining the number cr(K_{m,n}) was suggested by Paul Turán and became known as Turán's Brick Factory Problem.

External links

O'Connor, John J.; Robertson, Edmund F., "Kazimierz Zarankiewicz", MacTutor History of Mathematics archive, University of St Andrews.

Zarankiewicz Crossing Number Conjecture at MathWorld

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