Micha_Perles Knowpia

Micha Asher Perles
Micha Asher Perles
Born	Jerusalem
Alma mater	Hebrew University
Known for	Perles configuration, Perles–Sauer–Shelah lemma, pumping lemma
	Scientific career
Fields	convexity, combinatorics, graph theory
Thesis	(1964)
Doctoral advisor	Branko Grünbaum
Doctoral students	Noga Alon, Gil Kalai, Nati Linial

Micha Asher Perles is an Israeli mathematician working in geometry, a professor emeritus at the Hebrew University.^[1] He earned his Ph.D. in 1964 from the Hebrew University, under the supervision of Branko Grünbaum.^[2] His contributions include:

The Perles configuration, a set of nine points in the Euclidean plane whose collinearities can be realized only by using irrational numbers as coordinates. Perles used this configuration to prove the existence of irrational polytopes in higher dimensions.^[3]
The Perles–Sauer–Shelah lemma, a result in extremal set theory whose proof was credited to Perles by Saharon Shelah.^[4]^[5]
The pumping lemma for context-free languages, a widely used method for proving that a language is not context-free that Perles discovered with Yehoshua Bar-Hillel and Eli Shamir.^[6]

Notable students of Perles include Noga Alon, Gil Kalai, and Nati Linial.^[2]

References

^ Faculty profile, Hebrew University, retrieved 2013-12-12.
^ ^a ^b Micha Perles at the Mathematics Genealogy Project
^ Grünbaum, Branko (2003), Convex polytopes, Graduate Texts in Mathematics, vol. 221 (Second ed.), New York: Springer-Verlag, pp. 93–95, ISBN 0-387-00424-6, MR 1976856.
^ Shelah, Saharon (1972), "A combinatorial problem; stability and order for models and theories in infinitary languages", Pacific Journal of Mathematics, 41: 247–261, doi:10.2140/pjm.1972.41.247, MR 0307903.
^ Kalai, Gil (September 28, 2008), "Extremal Combinatorics III: Some Basic Theorems", Combinatorics and More.
^ Dewdney, A. K. (1993), The New Turing Omnibus: Sixty-Six Excursions in Computer Science, Macmillan, p. 91, ISBN 9780805071665.