Hazel Perfect

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 ${\displaystyle n\times n}$ matrices this region is the union of regular polygons of up to ${\displaystyle n}$ sides, having the roots of unity of each degree up to ${\displaystyle n}$ as vertices. Perfect and Mirsky proved their conjecture for ${\displaystyle n\leq 3}$; it was subsequently shown to be true for ${\displaystyle n=4}$ and false for ${\displaystyle n=5}$, but remains open for larger values of ${\displaystyle n}$.[9]^[SP2]

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]