Abraham Ziv (–) was an Israeli mathematician, known for his contributions to the

Zero-sum problem In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group ''G'' and a positive integer ''n'', one asks for the smallest value of ''k'' suc ...

as one of the discoverers of the

Erdős–Ginzburg–Ziv theorem In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group ''G'' and a positive integer ''n'', one asks for the smallest value of ''k'' suc ...

Biography

Abraham Zubkowski (later Ziv) was born in

Avihayil Avihayil (, lit. ''Father of strength'') is a moshav in central Israel. Located to the north-east of Netanya, it falls under the jurisdiction of Hefer Valley Regional Council. In it had a population of . Name The moshav was named after the bio ...

to Haim and Zila Zubkovski. In the 1950s, he changed his surname in the 1950s as part of the widespread

Hebraization of surnames The Hebraization of surnames (also Hebraicization) ( he, עברות, ''Ivrut'', "Hebraization") is the act of adopting a Hebrew surname in exchange for a diaspora name. For many diaspora Jews who migrated to Israel, taking a Hebrew surname was ...

trend. He studied at the

Technion – Israel Institute of Technology The Technion – Israel Institute of Technology ( he, הטכניון – מכון טכנולוגי לישראל) is a public research university located in Haifa, Israel. Established in 1912 under the dominion of the Ottoman Empire, the Technion ...

, where he earned his Ph.D. in mathematics, after receiving his master's degree from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

Academic career

In 1961, at the age of 21, Ziv proved along with

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

and

Abraham Ginzburg Abraham Ginzburg (1926–2020) was a Professor Emeritus of Computer Science. He served as Vice President of the Technion Institute, and President of the Open University of Israel Biography Ginzburg was born on 1 August 1926 in Navahrudak, Belar ...

the general result that every sequence of

2n - 1\

elements of

\mathbb/n\mathbb

contains

n

terms that sum to zero. In 1972 Ziv was part of the founding team of IBM R&D Labs in Israel, where he stayed until retirement. In his time at IBM he wrote 21 more publications and 6 patents.

Academic papers

References

External links

* * PlanetMat
Erdős, Ginzburg, Ziv Theorem
{{DEFAULTSORT:Ziv, Abraham 20th-century Israeli mathematicians Israeli Jews Harvard Graduate School of Arts and Sciences alumni 1940 births 2013 deaths Technion – Israel Institute of Technology alumni