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Hazel Perfect
British mathematician

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

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Contributions

Perfect was known for inventing gammoids,23[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 n × n {\displaystyle n\times n} matrices this region is the union of regular polygons of up to n {\displaystyle n} sides, having the roots of unity of each degree up to n {\displaystyle n} as vertices. Perfect and Mirsky proved their conjecture for n ≤ 3 {\displaystyle n\leq 3} ; it was subsequently shown to be true for n = 4 {\displaystyle n=4} and false for n = 5 {\displaystyle n=5} , but remains open for larger values of n {\displaystyle n} .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 015521014
TIA.Perfect, Hazel (1966), Topics in Algebra, Pergamon15
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 060417316

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, 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

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 009936117

References

  1. "Obituaries" (PDF), Newsletter of the London Mathematical Society, p. 41, December 2015 https://www.lms.ac.uk/sites/lms.ac.uk/files/files/December%202015.pdf ↩

  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 3-540-44389-4 ↩

  3. Welsh, D. J. A. (1976), Matroid theory, London and New York: Academic Press, p. 219, ISBN 9780486474397, MR 0427112 9780486474397 ↩

  4. O'Connor, John J.; Robertson, Edmund F., "Leon Mirsky", MacTutor History of Mathematics Archive, University of St Andrews /wiki/Edmund_F._Robertson ↩

  5. 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) /wiki/MR_(identifier) ↩

  6. 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) /wiki/JSTOR_(identifier) ↩

  7. 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) /wiki/Zbl_(identifier) ↩

  8. 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) /wiki/J._A._Todd ↩

  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 /wiki/Proceedings_of_the_American_Mathematical_Society ↩

  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 https://books.google.com/books?id=ou0aAQAAMAAJ ↩

  11. Burkill, H. (January 1999), "Gordon Marshall Petersen", Bulletin of the London Mathematical Society, 31 (1): 97–107, doi:10.1112/s0024609398005177 /wiki/Doi_(identifier) ↩

  12. Theses and Dissertations Accepted for Higher Degrees, University of London, 1967, p. 42 – via Google Books https://books.google.com/books?id=-DTgAAAAMAAJ ↩

  13. Author biography from A Mathematical Spectrum Miscellany: selections from Mathematical Spectrum, 1967–1994, Applied Probability Trust, 2000, p. 3, ISBN 9780902016057 9780902016057 ↩

  14. 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) /wiki/MR_(identifier) ↩

  15. 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) /wiki/JSTOR_(identifier) ↩

  16. 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) /wiki/Zbl_(identifier) ↩

  17. 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) /wiki/J._A._Todd ↩