Hazel Perfect

Perfect was known for inventing gammoids,{{r|schrijver|welsh}}{{ran|AMG}} for her work with Leon Mirsky on doubly stochastic matrices,{{r|mirsky}}{{ran|SP2}} for her three books Topics in Geometry,{{r|tig}}{{ran|TIG}} Topics in Algebra,{{r|tia}}{{ran|TIA}} and Independence Theory in Combinatorics,{{r|itc}}{{ran|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).{{r|itg}}{{ran|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 $n\backslash times\; n$ 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 $n\backslash le\; 3$; it was subsequently shown to be true for $n=4$ and false for $n=5$, but remains open for larger values {{nowrap|of $n$.{{r|lpk}}{{ran|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.{{r|westfield}}

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.{{r|petersen}}

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.{{r|uol}} She became a reader in mathematics at the University of Sheffield.{{r|spectrum}}

{{rma|TIG|tw=3em|{{citation

| last = Perfect | first = Hazel

| mr = 0155210

| publisher = Pergamon

| title = Topics in Geometry

| year = 1963}}{{r|tig}}}}

{{rma|TIA|tw=3em|{{citation

| last = Perfect | first = Hazel

| publisher = Pergamon

| title = Topics in Algebra

| year = 1966}}{{r|tia}}}}

{{rma|ITC|tw=3em|{{citation

| last1 = Bryant | first1 = Victor

| last2 = Perfect | first2 = Hazel

| isbn = 0-412-16220-2

| mr = 604173

| publisher = Chapman & Hall | location = London and New York

| title = Independence Theory in Combinatorics: An introductory account with applications to graphs and transversals

| title-link = Independence Theory in Combinatorics

| year = 1980}}{{r|itc}}}}

{{rma|SP2|tw=3em|{{citation

| last1 = Perfect | first1 = Hazel

| last2 = Mirsky | first2 = L. | author2-link = Leon Mirsky

| doi = 10.1007/BF01313442

| journal = Monatshefte für Mathematik

| mr = 0175917

| pages = 35–57

| title = Spectral properties of doubly-stochastic matrices

| volume = 69

| year = 1965| s2cid = 120466093

}}}}

{{rma|AMG|tw=3em|{{citation

| last = Perfect | first = Hazel

| doi = 10.1016/0022-247X(68)90163-7

| journal = Journal of Mathematical Analysis and Applications

| mr = 0224494

| pages = 96–111

| title = Applications of Menger's graph theorem

| volume = 22

| year = 1968| doi-access = free

}}}}

{{rma|ITG|tw=3em|{{citation

| last = Alexandroff | first = P. S. | authorlink = Pavel Alexandrov

| translator1-last = Perfect | translator1-first = Hazel

| translator2-last = Petersen | translator2-first = G. M.

| mr = 0099361

| publisher = Hafner Publishing Co. | location = New York

| title = An Introduction to the Theory of Groups

| year = 1959}}{{r|itg}}}}

{{reflist|refs=

Reviews of Independence Theory in Combinatorics:

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Reviews of An Introduction to the Theory of Groups:

• {{citation

| last = Todd | first = J. A. | authorlink = J. A. Todd

| date = July 1959

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}}

{{mactutor|id=Mirsky|title=Leon Mirsky}}

{{citation|url=https://www.lms.ac.uk/sites/lms.ac.uk/files/files/December%202015.pdf|magazine=Newsletter of the London Mathematical Society|date=December 2015|page=41|title=Obituaries}}

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{{citation

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| year = 2003}}

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Reviews of Topics in Algebra:

• {{citation

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| date = November 1968

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| title = none

| volume = 53}}

Review of Topics in Geometry:

• {{citation|first=G. M.|last=Petersen|journal=Mathematical Reviews|mr=0155210|title=none}}
• {{citation

| last = Primrose | first = E. J. F.

| date = December 1964

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• {{citation

| last = Garner | first = C. W. L.

| date = February 1965

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{{citation|page=42|title=Theses and Dissertations Accepted for Higher Degrees|publisher=University of London|via=Google Books|url=https://books.google.com/books?id=-DTgAAAAMAAJ|year=1967}}

{{citation

| last = Welsh | first = D. J. A. | authorlink = Dominic Welsh

| mr = 0427112

| page = 219

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| title = Matroid theory

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| year = 1976| isbn = 9780486474397 }}

{{citation|title=Subjects of Dissertations, Theses and Published Works Presented by Successful Candidates at Examinations for Higher Degrees|publisher=University of London|page=22|url=https://books.google.com/books?id=ou0aAQAAMAAJ|via=Google Books|year=1937}}

}}

{{Authority control}}

{{DEFAULTSORT:Perfect, Hazel}}

Category:2015 deaths

Category:British mathematicians

Category:British women mathematicians

Category:Alumni of Westfield College

Category:Academics of Swansea University

Category:Academics of the University of Sheffield

Category:German–English translators

Category:Technical translators

Category:Combinatorialists

Category:Year of birth uncertain