Hazel Perfect

Hazel Perfect (died 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 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

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, MR 0155210[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, MR 0604173[7]

Research papers
SP2.Perfect, Hazel; Mirsky, L. (1965), "Spectral properties of doubly-stochastic matrices", Monatshefte für Mathematik, 69: 35–57, doi:10.1007/BF01313442, MR 0175917
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
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]
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References
  1. "Hazel Perfect Obituary", The Star, 22 July 2015 – via Legacy.com
  2. Schrijver, Alexander (2003), Combinatorial optimization: Polyhedra and efficiency, Vol. B: Matroids, trees, stable sets, Algorithms and Combinatorics, 24, Berlin: Springer-Verlag, p. 659, ISBN 3-540-44389-4, MR 1956925
  3. Welsh, D. J. A. (1976), Matroid theory, London and New York: Academic Press, p. 219, ISBN 9780486474397, MR 0427112
  4. O'Connor, John J.; Robertson, Edmund F., "Leon Mirsky", MacTutor History of Mathematics archive, University of St Andrews.
  5. Review of Topics in Geometry:
    • Petersen, G. M., Mathematical Reviews, MR 0155210CS1 maint: untitled periodical (link)
    • Primrose, E. J. F. (December 1964), The Mathematical Gazette, 48 (366): 459, doi:10.1017/s0025557200051627CS1 maint: untitled periodical (link)
    • Garner, C. W. L. (February 1965), Canadian Mathematical Bulletin, 8 (1): 126–127, doi:10.1017/S0008439500024450CS1 maint: untitled periodical (link)
  6. Reviews of Topics in Algebra:
    • Drechsel, Robert R. (November 1968), The Mathematics Teacher, 61 (7): 725–726, JSTOR 27957974CS1 maint: untitled periodical (link)
    • Matthews, Geoffrey (December 1969), The Mathematical Gazette, 53 (386): 431–432, doi:10.2307/3612506, JSTOR 3612506CS1 maint: untitled periodical (link)
  7. Reviews of Independence Theory in Combinatorics:
  8. Reviews of An Introduction to the Theory of Groups:
    • Todd, J. A. (July 1959), Science Progress, 47 (187): 575, JSTOR 43417168CS1 maint: untitled periodical (link)
    • Hopkins, M. R. (March 1960), Physics Bulletin, 11 (3): 80, doi:10.1088/0031-9112/11/3/029CS1 maint: untitled periodical (link)
    • Johnson, R. E. (April 1960), The American Mathematical Monthly, 67 (4): 395, doi:10.2307/2309016, JSTOR 2309016CS1 maint: untitled periodical (link)
  9. 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
  10. 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
  11. Burkill, H. (January 1999), "Gordon Marshall Petersen", Bulletin of the London Mathematical Society, 31 (1): 97–107, doi:10.1112/s0024609398005177
  12. Theses and Dissertations Accepted for Higher Degrees, University of London, 1967, p. 42 – via Google Books
  13. 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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