Hazel Perfect (circa 1927 – 8 July 2015)[1] was a British mathematician specialising in combinatorics.
Contributions
editPerfect 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 matrices this region is the union of regular polygons of up to sides, having the roots of unity of each degree up to as vertices. Perfect and Mirsky proved their conjecture for ; it was subsequently shown to be true for and false for , but remains open for larger values of .[9][SP2]
Education and career
editPerfect 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
editBooks
edit| TIG. |
| 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, MR 0604173[7]
|
Research papers
edit| SP2. | Perfect, Hazel; Mirsky, L. (1965), "Spectral properties of doubly-stochastic matrices", Monatshefte für Mathematik, 69: 35–57, doi:10.1007/BF01313442, MR 0175917, S2CID 120466093
|
| AMG. | Perfect, Hazel (1968), "Applications of Menger's graph theorem", Journal of Mathematical Analysis and Applications, 22: 96–111, doi:10.1016/0022-247X(68)90163-7, MR 0224494
|
Translation
edit| ITG. | Alexandroff, P. S. (1959), An Introduction to the Theory of Groups, translated by Perfect, Hazel; Petersen, G. M., New York: Hafner Publishing Co., MR 0099361[8]
|
References
edit- ^ "Obituaries" (PDF), Newsletter of the London Mathematical Society, p. 41, December 2015
- ^ Schrijver, Alexander (2003), Combinatorial optimization: Polyhedra and efficiency, Vol. B: Matroids, trees, stable sets, Algorithms and Combinatorics, vol. 24, Berlin: Springer-Verlag, p. 659, ISBN 3-540-44389-4, MR 1956925
- ^ Welsh, D. J. A. (1976), Matroid theory, London and New York: Academic Press, p. 219, ISBN 9780486474397, MR 0427112
- ^ O'Connor, John J.; Robertson, Edmund F., "Leon Mirsky", MacTutor History of Mathematics Archive, University of St Andrews
- ^ a b Review of Topics in Geometry:
- Petersen, G. M., Mathematical Reviews, MR 0155210
{{citation}}: CS1 maint: untitled periodical (link) - Primrose, E. J. F. (December 1964), The Mathematical Gazette, 48 (366): 459, doi:10.1017/s0025557200051627
{{citation}}: CS1 maint: untitled periodical (link) - Garner, C. W. L. (February 1965), Canadian Mathematical Bulletin, 8 (1): 126–127, doi:10.1017/S0008439500024450
{{citation}}: CS1 maint: untitled periodical (link)
- Petersen, G. M., Mathematical Reviews, MR 0155210
- ^ a b Reviews of Topics in Algebra:
- Drechsel, Robert R. (November 1968), The Mathematics Teacher, 61 (7): 725–726, JSTOR 27957974
{{citation}}: CS1 maint: untitled periodical (link) - Matthews, Geoffrey (December 1969), The Mathematical Gazette, 53 (386): 431–432, doi:10.2307/3612506, JSTOR 3612506
{{citation}}: CS1 maint: untitled periodical (link)
- Drechsel, Robert R. (November 1968), The Mathematics Teacher, 61 (7): 725–726, JSTOR 27957974
- ^ a b Reviews of Independence Theory in Combinatorics:
- Dörfler, W., zbMATH, Zbl 0435.05017
{{citation}}: CS1 maint: untitled periodical (link) - Rado, Richard (May 1981), Bulletin of the London Mathematical Society, 13 (3), Wiley: 252–253, doi:10.1112/blms/13.3.252
{{citation}}: CS1 maint: untitled periodical (link) - Welsh, D. J. A. (October 1981), The Mathematical Gazette, 65 (433): 228, doi:10.2307/3617158, JSTOR 3617158
{{citation}}: CS1 maint: untitled periodical (link) - Lloyd, E. Keith (1982), Mathematical Reviews, MR 0604173
{{citation}}: CS1 maint: untitled periodical (link) - Korte, Bernhard (January 1982), European Journal of Operational Research, 9 (1): 100–101, doi:10.1016/0377-2217(82)90025-x
{{citation}}: CS1 maint: untitled periodical (link) - Ganley, Michael J. (October 1982), Proceedings of the Edinburgh Mathematical Society, 25 (3): 282, doi:10.1017/s0013091500016795
{{citation}}: CS1 maint: untitled periodical (link)
- Dörfler, W., zbMATH, Zbl 0435.05017
- ^ a b Reviews of An Introduction to the Theory of Groups:
- Todd, J. A. (July 1959), Science Progress, 47 (187): 575, JSTOR 43417168
{{citation}}: CS1 maint: untitled periodical (link) - Hopkins, M. R. (March 1960), Physics Bulletin, 11 (3): 80, doi:10.1088/0031-9112/11/3/029
{{citation}}: CS1 maint: untitled periodical (link) - Johnson, R. E. (April 1960), The American Mathematical Monthly, 67 (4): 395, doi:10.2307/2309016, JSTOR 2309016
{{citation}}: CS1 maint: untitled periodical (link)
- Todd, J. A. (July 1959), Science Progress, 47 (187): 575, JSTOR 43417168
- ^ 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, MR 3314105
- ^ Subjects of Dissertations, Theses and Published Works Presented by Successful Candidates at Examinations for Higher Degrees, University of London, 1937, p. 22 – via Google Books
- ^ 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 – via Google Books
- ^ Author biography from A Mathematical Spectrum Miscellany: selections from Mathematical Spectrum, 1967–1994, Applied Probability Trust, 2000, p. 3, ISBN 9780902016057