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Hazel Perfect
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<h2 id="contributions">Contributions</h2> <p>Perfect was known for inventing <a href="/facts/Gammoid/M1GRIXzP">gammoids</a>,<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>[AMG] for her work with <a href="/facts/Leon_Mirsky/34wvkuDt">Leon Mirsky</a> on <a href="/facts/Doubly_stochastic_matrix/IwqKyx05">doubly stochastic matrices</a>,<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>[SP2] for her three books <i>Topics in Geometry</i>,<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>[TIG] <i>Topics in Algebra</i>,<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>[TIA] and <i><a href="/facts/Independence_Theory_in_Combinatorics/4pJaa2lQ">Independence Theory in Combinatorics</a></i>,<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a>[ITC] and for her work as a translator (from an earlier German translation) of <a href="/facts/Pavel_Alexandrov/booz6U09">Pavel Alexandrov</a>'s book <i>An Introduction to the Theory of Groups</i> (Hafner, 1959).<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a>[ITG] </p><p>The Perfect–Mirsky conjecture, named after Perfect and <a href="/facts/Leon_Mirsky/34wvkuDt">Leon Mirsky</a>, concerns the region of the <a href="/facts/Complex_plane/vE0QrxJp">complex plane</a> formed by the <a href="/facts/Eigenvalue/8TjEoT8u">eigenvalues</a> 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 <a href="/facts/Root_of_unity/EqH0ho1Y">roots of unity</a> 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} .<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a>[SP2] </p> <h2 id="education-and-career">Education and career</h2> <p>Perfect earned a master's degree through <a href="/facts/Westfield_College/6ePVWssx">Westfield College</a> (a constituent college for women in the <a href="/facts/University_of_London/spIRAx9B">University of London</a>) in 1949, with a thesis on <i>The Reduction of Matrices to Canonical Form</i>.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> In the 1950s, Perfect was a lecturer at <a href="/facts/Swansea_University/l4bJFYsq">University College of Swansea</a>; she collaborated with Gordon Petersen, a visitor to Swansea at that time, on their translation of Alexandrov's book.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> She completed her Ph.D. at the University of London in 1969; her dissertation was <i>Studies in Transversal Theory with Particular Reference to Independence Structures and Graphs</i>.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> She became a reader in mathematics at the <a href="/facts/University_of_Sheffield/YBEItxSg">University of Sheffield</a>.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> </p> <h2 id="selected-publications">Selected publications</h2> <h3>Books</h3> <table><tbody><tr><td scope="col">TIG.</td><td>Perfect, Hazel (1963), <i>Topics in Geometry</i>, Pergamon, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0155210">0155210</a><a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></td></tr></tbody></table> <table><tbody><tr><td scope="col">TIA.</td><td>Perfect, Hazel (1966), <i>Topics in Algebra</i>, Pergamon<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></td></tr></tbody></table> <table><tbody><tr><td scope="col">ITC.</td><td>Bryant, Victor; Perfect, Hazel (1980), <a href="/facts/Independence_Theory_in_Combinatorics/4pJaa2lQ"><i>Independence Theory in Combinatorics: An introductory account with applications to graphs and transversals</i></a>, London and New York: Chapman & Hall, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-412-16220-2, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0604173">0604173</a><a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></td></tr></tbody></table> <h3>Research papers</h3> <table><tbody><tr><td scope="col">SP2.</td><td>Perfect, Hazel; <a href="/facts/Leon_Mirsky/34wvkuDt">Mirsky, L.</a> (1965), "Spectral properties of doubly-stochastic matrices", <i><a href="/facts/Monatshefte_f%C3%BCr_Mathematik/9TBp5nl3">Monatshefte für Mathematik</a></i>, 69: 35–57, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01313442">10.1007/BF01313442</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0175917">0175917</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:120466093">120466093</a></td></tr></tbody></table> <table><tbody><tr><td scope="col">AMG.</td><td>Perfect, Hazel (1968), "Applications of Menger's graph theorem", <i><a href="/facts/Journal_of_Mathematical_Analysis_and_Applications/IeXhWStY">Journal of Mathematical Analysis and Applications</a></i>, 22: 96–111, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2F0022-247X%2868%2990163-7">10.1016/0022-247X(68)90163-7</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0224494">0224494</a></td></tr></tbody></table> <h3>Translation</h3> <table><tbody><tr><td scope="col">ITG.</td><td><a href="/facts/Pavel_Alexandrov/booz6U09">Alexandroff, P. S.</a> (1959), <i>An Introduction to the Theory of Groups</i>, translated by Perfect, Hazel; Petersen, G. M., New York: Hafner Publishing Co., <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0099361">0099361</a><a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a></td></tr></tbody></table> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"Obituaries" (PDF), Newsletter of the London Mathematical Society, p. 41, December 2015 <a href="https://www.lms.ac.uk/sites/lms.ac.uk/files/files/December%202015.pdf" target="_blank">https://www.lms.ac.uk/sites/lms.ac.uk/files/files/December%202015.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Schrijver, Alexander (2003), Combinatorial optimization: Polyhedra and efficiency, Vol. B: Matroids, trees, stable sets, Algorithms and Combinatorics, vol. 24, Berlin: Springer-Verlag, p. 659, ISBN 3-540-44389-4, MR 1956925 <a href="3-540-44389-4" target="_blank">3-540-44389-4</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Welsh, D. J. A. (1976), Matroid theory, London and New York: Academic Press, p. 219, ISBN 9780486474397, MR 0427112 <a href="9780486474397" target="_blank">9780486474397</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>O'Connor, John J.; Robertson, Edmund F., "Leon Mirsky", MacTutor History of Mathematics Archive, University of St Andrews <a href="/wiki/Edmund_F._Robertson" target="_blank">/wiki/Edmund_F._Robertson</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Review of Topics in Geometry: Petersen, G. M., Mathematical Reviews, MR 0155210{{citation}}: CS1 maint: untitled periodical (link) Primrose, E. J. F. (December 1964), The Mathematical Gazette, 48 (366): 459, doi:10.1017/s0025557200051627{{citation}}: CS1 maint: untitled periodical (link) Garner, C. W. L. (February 1965), Canadian Mathematical Bulletin, 8 (1): 126–127, doi:10.1017/S0008439500024450{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/MR_(identifier)" target="_blank">/wiki/MR_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Reviews of Topics in Algebra: Drechsel, Robert R. (November 1968), The Mathematics Teacher, 61 (7): 725–726, JSTOR 27957974{{citation}}: CS1 maint: untitled periodical (link) Matthews, Geoffrey (December 1969), The Mathematical Gazette, 53 (386): 431–432, doi:10.2307/3612506, JSTOR 3612506{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/JSTOR_(identifier)" target="_blank">/wiki/JSTOR_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Reviews of Independence Theory in Combinatorics: Dörfler, W., zbMATH, Zbl 0435.05017{{citation}}: CS1 maint: untitled periodical (link) Rado, Richard (May 1981), Bulletin of the London Mathematical Society, 13 (3), Wiley: 252–253, doi:10.1112/blms/13.3.252{{citation}}: CS1 maint: untitled periodical (link) Welsh, D. J. A. (October 1981), The Mathematical Gazette, 65 (433): 228, doi:10.2307/3617158, JSTOR 3617158{{citation}}: CS1 maint: untitled periodical (link) Lloyd, E. Keith (1982), Mathematical Reviews, MR 0604173{{citation}}: CS1 maint: untitled periodical (link) Korte, Bernhard (January 1982), European Journal of Operational Research, 9 (1): 100–101, doi:10.1016/0377-2217(82)90025-x{{citation}}: CS1 maint: untitled periodical (link) Ganley, Michael J. (October 1982), Proceedings of the Edinburgh Mathematical Society, 25 (3): 282, doi:10.1017/s0013091500016795{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/Zbl_(identifier)" target="_blank">/wiki/Zbl_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Reviews of An Introduction to the Theory of Groups: Todd, J. A. (July 1959), Science Progress, 47 (187): 575, JSTOR 43417168{{citation}}: CS1 maint: untitled periodical (link) Hopkins, M. R. (March 1960), Physics Bulletin, 11 (3): 80, doi:10.1088/0031-9112/11/3/029{{citation}}: CS1 maint: untitled periodical (link) Johnson, R. E. (April 1960), The American Mathematical Monthly, 67 (4): 395, doi:10.2307/2309016, JSTOR 2309016{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/J._A._Todd" target="_blank">/wiki/J._A._Todd</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Levick, Jeremy; Pereira, Rajesh; Kribs, David W. (2015), "The four-dimensional Perfect–Mirsky Conjecture", Proceedings of the American Mathematical Society, 143 (5): 1951–1956, doi:10.1090/S0002-9939-2014-12412-9, MR 3314105 <a href="/wiki/Proceedings_of_the_American_Mathematical_Society" target="_blank">/wiki/Proceedings_of_the_American_Mathematical_Society</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Subjects of Dissertations, Theses and Published Works Presented by Successful Candidates at Examinations for Higher Degrees, University of London, 1937, p. 22 – via Google Books <a href="https://books.google.com/books?id=ou0aAQAAMAAJ" target="_blank">https://books.google.com/books?id=ou0aAQAAMAAJ</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Burkill, H. (January 1999), "Gordon Marshall Petersen", Bulletin of the London Mathematical Society, 31 (1): 97–107, doi:10.1112/s0024609398005177 <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Theses and Dissertations Accepted for Higher Degrees, University of London, 1967, p. 42 – via Google Books <a href="https://books.google.com/books?id=-DTgAAAAMAAJ" target="_blank">https://books.google.com/books?id=-DTgAAAAMAAJ</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Author biography from A Mathematical Spectrum Miscellany: selections from Mathematical Spectrum, 1967–1994, Applied Probability Trust, 2000, p. 3, ISBN 9780902016057 <a href="9780902016057" target="_blank">9780902016057</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Review of Topics in Geometry: Petersen, G. M., Mathematical Reviews, MR 0155210{{citation}}: CS1 maint: untitled periodical (link) Primrose, E. J. F. (December 1964), The Mathematical Gazette, 48 (366): 459, doi:10.1017/s0025557200051627{{citation}}: CS1 maint: untitled periodical (link) Garner, C. W. L. (February 1965), Canadian Mathematical Bulletin, 8 (1): 126–127, doi:10.1017/S0008439500024450{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/MR_(identifier)" target="_blank">/wiki/MR_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Reviews of Topics in Algebra: Drechsel, Robert R. (November 1968), The Mathematics Teacher, 61 (7): 725–726, JSTOR 27957974{{citation}}: CS1 maint: untitled periodical (link) Matthews, Geoffrey (December 1969), The Mathematical Gazette, 53 (386): 431–432, doi:10.2307/3612506, JSTOR 3612506{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/JSTOR_(identifier)" target="_blank">/wiki/JSTOR_(identifier)</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Reviews of Independence Theory in Combinatorics: Dörfler, W., zbMATH, Zbl 0435.05017{{citation}}: CS1 maint: untitled periodical (link) Rado, Richard (May 1981), Bulletin of the London Mathematical Society, 13 (3), Wiley: 252–253, doi:10.1112/blms/13.3.252{{citation}}: CS1 maint: untitled periodical (link) Welsh, D. J. A. (October 1981), The Mathematical Gazette, 65 (433): 228, doi:10.2307/3617158, JSTOR 3617158{{citation}}: CS1 maint: untitled periodical (link) Lloyd, E. Keith (1982), Mathematical Reviews, MR 0604173{{citation}}: CS1 maint: untitled periodical (link) Korte, Bernhard (January 1982), European Journal of Operational Research, 9 (1): 100–101, doi:10.1016/0377-2217(82)90025-x{{citation}}: CS1 maint: untitled periodical (link) Ganley, Michael J. (October 1982), Proceedings of the Edinburgh Mathematical Society, 25 (3): 282, doi:10.1017/s0013091500016795{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/Zbl_(identifier)" target="_blank">/wiki/Zbl_(identifier)</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Reviews of An Introduction to the Theory of Groups: Todd, J. A. (July 1959), Science Progress, 47 (187): 575, JSTOR 43417168{{citation}}: CS1 maint: untitled periodical (link) Hopkins, M. R. (March 1960), Physics Bulletin, 11 (3): 80, doi:10.1088/0031-9112/11/3/029{{citation}}: CS1 maint: untitled periodical (link) Johnson, R. E. (April 1960), The American Mathematical Monthly, 67 (4): 395, doi:10.2307/2309016, JSTOR 2309016{{citation}}: CS1 maint: untitled periodical (link) <a href="/wiki/J._A._Todd" target="_blank">/wiki/J._A._Todd</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> </ol>