Short description: British mathematician
Hazel Perfect (circa 1927 – 8 July 2015)[1] was a British mathematician specialising in combinatorics.
Contributions
Perfect was known for inventing gammoids,[2][3][AMG] for her work with Leon Mirsky on doubly stochastic matrices,[4][SP2] for her three books Topics in Geometry,[5][TIG] Topics in Algebra,[6][TIA] and Independence Theory in Combinatorics,[7][ITC] and for her work as a translator (from an earlier German translation) of Pavel Alexandrov's book An Introduction to the Theory of Groups (Hafner, 1959).[8][ITG]
The Perfect–Mirsky conjecture, named after Perfect and Leon Mirsky, concerns the region of the complex plane formed by the eigenvalues of doubly stochastic matrices. Perfect and Mirsky conjectured that for [math]\displaystyle{ n\times n }[/math] matrices this region is the union of regular polygons of up to [math]\displaystyle{ n }[/math] sides, having the roots of unity of each degree up to [math]\displaystyle{ n }[/math] as vertices. Perfect and Mirsky proved their conjecture for [math]\displaystyle{ n\le 3 }[/math]; it was subsequently shown to be true for [math]\displaystyle{ n=4 }[/math] and false for [math]\displaystyle{ n=5 }[/math], but remains open for larger values of [math]\displaystyle{ n }[/math].[9][SP2]
Education and career
Perfect earned a master's degree through Westfield College (a constituent college for women in the University of London) in 1949, with a thesis on The Reduction of Matrices to Canonical Form.[10]
In the 1950s, Perfect was a lecturer at University College of Swansea; she collaborated with Gordon Petersen, a visitor to Swansea at that time, on their translation of Alexandrov's book.[11]
She completed her Ph.D. at the University of London in 1969; her dissertation was Studies in Transversal Theory with Particular Reference to Independence Structures and Graphs.[12] She became a reader in mathematics at the University of Sheffield.[13]
Selected publications
Books
| TIG. |
Perfect, Hazel (1963), Topics in Geometry, Pergamon [5]
|
| TIA. |
Perfect, Hazel (1966), Topics in Algebra, Pergamon [6]
|
| ITC. |
Bryant, Victor; Perfect, Hazel (1980), Independence Theory in Combinatorics: An introductory account with applications to graphs and transversals, London and New York: Chapman & Hall, ISBN 0-412-16220-2 [7]
|
Research papers
Translation
| ITG. |
An Introduction to the Theory of Groups, New York: Hafner Publishing Co., 1959 [8]
|
References
- ↑ "Obituaries", Newsletter of the London Mathematical Society: 41, December 2015, https://www.lms.ac.uk/sites/lms.ac.uk/files/files/December%202015.pdf
- ↑ Combinatorial optimization: Polyhedra and efficiency, Vol. B: Matroids, trees, stable sets, Algorithms and Combinatorics, 24, Berlin: Springer-Verlag, 2003, p. 659, ISBN 3-540-44389-4, https://books.google.com/books?id=mqGeSQ6dJycC&pg=PA659
- ↑ Matroid theory, London and New York: Academic Press, 1976, p. 219, ISBN 9780486474397, https://books.google.com/books?id=QL2iYMBLpFwC&pg=PA219
- ↑ O'Connor, John J.; Robertson, Edmund F., "Leon Mirsky", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Mirsky.html .
- ↑ 5.0 5.1 Review of Topics in Geometry:
- Petersen, G. M., "none", Mathematical Reviews
- Primrose, E. J. F. (December 1964), "none", The Mathematical Gazette 48 (366): 459, doi:10.1017/s0025557200051627
- Garner, C. W. L. (February 1965), "none", Canadian Mathematical Bulletin 8 (1): 126–127, doi:10.1017/S0008439500024450
- ↑ 6.0 6.1 Reviews of Topics in Algebra:
- Drechsel, Robert R. (November 1968), "none", The Mathematics Teacher 61 (7): 725–726
- Matthews, Geoffrey (December 1969), "none", The Mathematical Gazette 53 (386): 431–432, doi:10.2307/3612506
- ↑ 7.0 7.1 Reviews of Independence Theory in Combinatorics:
- Dörfler, W., "none", zbMATH
- "none", Bulletin of the London Mathematical Society (Wiley) 13 (3): 252–253, May 1981, doi:10.1112/blms/13.3.252
- "none", The Mathematical Gazette 65 (433): 228, October 1981, doi:10.2307/3617158
- Lloyd, E. Keith (1982), "none", Mathematical Reviews
- "none", European Journal of Operational Research 9 (1): 100–101, January 1982, doi:10.1016/0377-2217(82)90025-x
- Ganley, Michael J. (October 1982), "none", Proceedings of the Edinburgh Mathematical Society 25 (3): 282, doi:10.1017/s0013091500016795
- ↑ 8.0 8.1 Reviews of An Introduction to the Theory of Groups:
- "none", Science Progress 47 (187): 575, July 1959
- Hopkins, M. R. (March 1960), "none", Physics Bulletin 11 (3): 80, doi:10.1088/0031-9112/11/3/029
- Johnson, R. E. (April 1960), "none", The American Mathematical Monthly 67 (4): 395, doi:10.2307/2309016
- ↑ Levick, Jeremy; Pereira, Rajesh; Kribs, David W. (2015), "The four-dimensional Perfect–Mirsky Conjecture", Proceedings of the American Mathematical Society 143 (5): 1951–1956, doi:10.1090/S0002-9939-2014-12412-9
- ↑ Subjects of Dissertations, Theses and Published Works Presented by Successful Candidates at Examinations for Higher Degrees, University of London, 1937, p. 22, https://books.google.com/books?id=ou0aAQAAMAAJ
- ↑ Burkill, H. (January 1999), "Gordon Marshall Petersen", Bulletin of the London Mathematical Society 31 (1): 97–107, doi:10.1112/s0024609398005177
- ↑ Theses and Dissertations Accepted for Higher Degrees, University of London, 1967, p. 42, https://books.google.com/books?id=-DTgAAAAMAAJ
- ↑ Author biography from A Mathematical Spectrum Miscellany: selections from Mathematical Spectrum, 1967–1994, Applied Probability Trust, 2000, p. 3, ISBN 9780902016057
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