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]