Hazel Perfect

Hazel Perfect (circa 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 $n\times n$ 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 $n\le 3$; 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

TIG.

TIA.

ITC.

Research papers

SP2.

AMG.

Translation

ITG.