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 × 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}.[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