The , 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, MR0155210[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, ISBN0-412-16220-2, MR0604173[7]
Alexandroff, P. S. (1959), An Introduction to the Theory of Groups, translated by Perfect, Hazel; Petersen, G. M., New York: Hafner Publishing Co., MR0099361[8]
^ Jump up to: abReviews of Independence Theory in Combinatorics:
Rado, Richard (May 1981), Bulletin of the London Mathematical Society, Wiley, 13 (3): 252–253, doi:10.1112/blms/13.3.252CS1 maint: untitled periodical (link)
Ganley, Michael J. (October 1982), Proceedings of the Edinburgh Mathematical Society, 25 (3): 282, doi:10.1017/s0013091500016795CS1 maint: untitled periodical (link)
^ Jump up to: abReviews of An Introduction to the Theory of Groups:
Todd, J. A. (July 1959), Science Progress, 47 (187): 575, JSTOR43417168CS1 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, JSTOR2309016CS1 maint: untitled periodical (link)
^Author biography from A Mathematical Spectrum Miscellany: selections from Mathematical Spectrum, 1967–1994, Applied Probability Trust, 2000, p. 3, ISBN9780902016057