Misplaced Pages

Kazimierz Zarankiewicz

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Polish mathematician (1902–1959)
Kazimierz Zarankiewicz
Zarankiewicz in Moscow 1935
Born(1902-05-02)2 May 1902
Częstochowa, Congress Poland, Russian Empire
Died5 September 1959(1959-09-05) (aged 57)
London, England
NationalityPolish
Alma materUniversity of Warsaw
Known forZarankiewicz problem
Zarankiewicz crossing number conjecture
Scientific career
FieldsTopology
Graph theory
InstitutionsUniversity of Warsaw

Kazimierz Zarankiewicz (2 May 1902 – 5 September 1959) was a Polish mathematician and Professor at the Warsaw University of Technology who was interested primarily in topology and graph theory.

Biography

Grave of Kazimierz Zarankiewicz in Powązki Cemetery, Warsaw

Zarankiewicz was born in Częstochowa to father Stanisław and mother Józefa (née Borowska). He studied at the University of Warsaw, together with Zygmunt Janiszewski, Stefan Mazurkiewicz, Wacław Sierpiński, Kazimierz Kuratowski, and Stanisław Saks.

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

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

He died in London, England.

Research contributions

Zarankiewicz wrote works on cut-points in connected spaces, on conformal mappings, on complex functions and number theory, and triangular numbers.

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 guarantee that the matrix contains at least one a × b submatrix is made up only of 1's. An equivalent formulation in extremal graph theory asks for the maximum number of edges in a bipartite graph with no complete bipartite subgraph Ka,b.

The Zarankiewicz crossing number conjecture in the mathematical field of graph theory is also named after Zarankiewicz. The conjecture states that the crossing number of a complete bipartite graph K m , n {\displaystyle K_{m,n}} equals

cr ( K m , n ) = ⌊ n 2 ⌋ ⌊ n − 1 2 ⌋ ⌊ m 2 ⌋ ⌊ m − 1 2 ⌋ .   {\displaystyle {\text{cr}}(K_{m,n})=\left\lfloor {\frac {n}{2}}\right\rfloor \left\lfloor {\frac {n-1}{2}}\right\rfloor \left\lfloor {\frac {m}{2}}\right\rfloor \left\lfloor {\frac {m-1}{2}}\right\rfloor .\ }

Zarankiewicz proved that this formula is an upper bound for the actual crossing number. The problem of determining the number c r ( K m , n ) {\displaystyle cr(K_{m,n})} was suggested by Paul Turán and became known as Turán's brick factory problem.

See also

References

  1. Wiesław Wójcik. "Zarankiewicz Kazimierz Józef". gigancinauki.pl (in Polish). Retrieved 2 February 2023.
  2. "Kazimierz Zarankiewicz". Retrieved 2 February 2023.

External links

Categories: