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Hazel Perfect
Hazel Perfect (circa 1927 – 8 July 2015) was a British mathematician specialising in combinatorics. Contributions Perfect was known for inventing gammoids, for her work with Leon Mirsky on doubly stochastic matrices, for her three books ''Topics in Geometry'', ''Topics in Algebra'', and '' Independence Theory in Combinatorics'', 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). 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 value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |