Hazel Perfect

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Hazel Perfect (circa 1927 – 8 July 2015)[1] was a British mathematician specialising in combinatorics.


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[edit]

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[edit]


Perfect, Hazel (1963), Topics in Geometry, Pergamon, MR 0155210[5]
Perfect, Hazel (1966), Topics in Algebra, Pergamon[6]

Research papers[edit]

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
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


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]


  1. ^ "Obituaries" (PDF), Newsletter of the London Mathematical Society, p. 41, December 2015
  2. ^ 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
  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. ^ a b Review of Topics in Geometry:
  6. ^ a b Reviews of Topics in Algebra:
  7. ^ a b Reviews of Independence Theory in Combinatorics:
  8. ^ a b Reviews of An Introduction to the Theory of Groups:
  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