Leonid Mirsky

Leonid Mirsky or Leon Mirsky (born December 19, 1918 , † December 1, 1983 in Sheffield , England ) was an English mathematician born in Russia .

Life and career

Mirsky was from Russia. The father was a doctor , the mother a dentist . From the age of 8 he lived separately from his parents with his uncle and aunt in Germany . He emigrated to England with them and lived in Bradford for a while . From 1936 to 1942 he studied at King's College London .

From 1942 he worked at the University of Sheffield , where he received his doctorate in 1949 . In 1971 he became a full professor there . In September 1983, he joined at the age of 64 into the retirement .

Mirsky had a deep friendship and close cooperation with the German mathematician Richard Rado , who also worked in Sheffield .

Mirsky was a member of the London Mathematical Society for more than 40 years .

Scientific achievements

Leonid Mirsky dealt mainly with pure mathematics . First he worked on questions of number theory and in particular on prime number problems and related questions. As a result of his teaching tasks, he then increasingly turned to linear algebra and examined the existence criteria of matrices with given diagonal elements and eigenvalues , double-stochastic matrices and zeros of real and complex polynomials . From around the mid-1960s he expanded his research to include questions of combinatorics . Here he examined the connection between the theory of matroids and the transversal theory , i.e. the mathematical structure of the (partial) representative systems of set families . Mirsky is considered one of the pioneers in this branch of mathematics .

Leonid Mirsky's name is associated with the following two mathematical theorems :

• Mirsky theorem : A partially ordered set , which for a given natural number does not contain a single chain with elements , can always be represented as a union of or fewer - anti- chains . ${\displaystyle (M,\leq )}$ ${\displaystyle m}$ ${\displaystyle (K,{\leq }|_{K})\subseteq (M,\leq )}$ ${\displaystyle m+1}$ ${\displaystyle m}$ ${\displaystyle \leq }$
• Farahat and Mirsky theorem : For a natural number , the Hamel dimension of the subspace generated by the permutation matrices is always the same in the real matrix space . ${\displaystyle n}$ ${\displaystyle {\mathbb {R} }^{n\times n}}$ ${\displaystyle n^{2}-2n+2}$

Fonts

Leonid Mirsky is the author or co-author of around 86 scientific papers . He is also the author of two monographs :

1. Leonid Mirsky: Transversal Theory . An Account of some Aspects of Combinatorial Mathematics (=  Mathematics in Science and Engineering . Volume 75 ). Academic Press , New York, London 1971. MR0282853
2. Leonid Mirsky: An Introduction to Linear Algebra . Reprint of the 1972 Edition. 2nd Edition. Dover Publications, Inc. , New York 1990, ISBN 0-486-66434-1 . MR1088257

swell

• Siegfried Gottwald , Hans-Joachim Ilgauds , Karl-Heinz Schlote (ed.): Lexicon of important mathematicians . Verlag Harri Deutsch, Thun 1990, ISBN 3-8171-1164-9 , p. 326 . MR1089881
• Harry Burkill , Walter Ledermann , Christopher Hooley , Hazel Perfect : Obituary: Leon Mirsky . In: The Bulletin of the London Mathematical Society . tape 18 , 1986, pp. 195–206 , doi : 10.1112 / blms / 18.2.195 . MR0818826

Web links

• Web link to the NNDB
• Entry in The Mathematics Genealogy Project

Individual evidence

1. ^ L. Mirsky: A dual of Dilworth's decomposition theorem . In: American Mathematical Monthly . tape 68 , 1971, p. 876-877 , doi : 10.2307 / 2316481 .
2. ↑ Dieter Jungnickel : Graphs, Networks and Algorithms . BI Wissenschaftsverlag , Mannheim (among others) 1987, ISBN 3-411-03126-3 , p. 158.161-162 .
3. ↑ HK Farahat , L. Mirsky: Permutation endomorphisms and refinement of a theorem of Birkhoff . In: Mathematical Proceedings of the Cambridge Philosophical Society . tape 56 , 1960, pp. 322-328 , doi : 10.1017 / S0305004100034629 .
4. ↑ Jungnickel, op.cit., P. 158