Hazel Perfect

Hazel Perfect (c. 1927 – 8 July 2015) was a British mathematician specialising in combinatorics.

Contributions

Perfect was known for inventing gammoids,[AMG] for her work with Leon Mirsky on doubly stochastic matrices,[SP2] for her three books Topics in Geometry,[TIG] Topics in Algebra,[TIA] and Independence Theory in Combinatorics,[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).[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 n×n matrices this region is the union of regular polygons of up to n sides, having the roots of unity of each degree up to n as vertices. Perfect and Mirsky proved their conjecture for n≤3; it was subsequently shown to be true for n=4 and false for n=5, but remains open for larger values of n.[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. 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. 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. She became a reader in mathematics at the University of Sheffield.

Selected publications

Books

Research papers

Translation

References

  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. 1 2 Review of Topics in Geometry:
  6. 1 2 Reviews of Topics in Algebra:
  7. 1 2 Reviews of Independence Theory in Combinatorics:
  8. 1 2 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