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Finally, in 1970 McMullen gave a complete proof of the upper-bound conjecture – since then it has been known as the upper bound theorem. McMullen's proof is amazingly simple and elegant, combining to key tools: shellability and
703:-vectors of convex polytopes is ... far from a solution, but there are important contributions towards it. For simplicial convex polytopes a characterization was proposed by McMullen in the form of his celebrated
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have the maximum possible number of faces among all polytopes with a given dimension and number of vertices. McMullen also formulated the g-conjecture, later the
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where he still works as a professor emeritus. In 2006 he was accepted as a corresponding member of the
Austrian Academy of Sciences.
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can be guaranteed to exist. It was credited to a private communication from McMullen in a 1972 paper by David G. Larman.
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605:, Special Collections, Wilson Library, Western Washington University, retrieved from worldcat.org 2013-11-03.
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He is also known for his 1960s drawing, by hand, of a 2-dimensional representation of the Gosset polytope 4
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is an unsolved question in discrete geometry named after McMullen, concerning the number of points in
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679:, Grundlehren der Mathematischen Wissenschaften , vol. 336, Berlin: Springer, p. 265,
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Larman, D. G. (1972), "On sets projectively equivalent to the vertices of a convex polytope",
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128:(born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at
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McMullen, P. (1970), "The maximum numbers of faces of a convex polytope",
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425:——; Schneider, Rolf (1983), "Valuations on convex bodies",
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Mathematical
Proceedings of the Cambridge Philosophical Society
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from 1968 to 1969. In 1978 he earned his Doctor of
Science at
800:, University College London, June 2006, retrieved 2013-11-03.
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Metrical and combinatorial properties of convex polytopes
148:, where he received his doctorate in 1968.. He taught at
711:-conjecture was proved by Billera and Lee and Stanley
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McMullen earned bachelor's and master's degrees from
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466:Convex Polytopes and the Upper Bound Conjecture
616:"Austrian Academy of Sciences: Peter McMullen"
371:—— (1993), "On simple polytopes",
798:Awards, Appointments, Elections & Honours
864:Fellows of the American Mathematical Society
869:Members of the Austrian Academy of Sciences
256:He was elected as a foreign member of the
241:McMullen was invited to speak at the 1974
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260:in 2006. In 2012 he became an inaugural
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849:Alumni of Trinity College, Cambridge
603:Peter McMullen Collection, 1967-1968
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761:. American Institute of Mathematics
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699:The problem of characterizing the
164:McMullen is known for his work in
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109:Western Washington University
676:Convex and discrete geometry
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258:Austrian Academy of Sciences
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559:UCL IRIS information system
440:Handbook of convex geometry
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488:Cambridge University Press
482:Abstract regular polytopes
176:. This result states that
142:Trinity College, Cambridge
68:Trinity College, Cambridge
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673:Gruber, Peter M. (2007),
348:10.1017/s0305004100051665
300:10.1112/s0025579300002850
216:projective transformation
154:University College London
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374:Inventiones Mathematicae
166:polyhedral combinatorics
146:University of Birmingham
19:Not to be confused with
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641:Lectures on Polytopes
462:Shephard, Geoffrey C.
272:Selected publications
192:, characterizing the
144:, and studied at the
16:British mathematician
779:ICM 1974 proceedings
136:Education and career
810:List of AMS fellows
387:1993InMat.113..419M
340:1975MPCPS..78..247M
188:, Carl W. Lee, and
174:upper bound theorem
78:Upper bound theorem
784:2017-12-04 at the
738:10.1112/blms/4.1.6
636:Ziegler, Günter M.
395:10.1007/BF01244313
237:Awards and honours
201:simplicial spheres
190:Richard P. Stanley
874:British geometers
707:-conjecture. The
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170:discrete geometry
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105:Institutions
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829:1942 births
286:Mathematika
111:(1968–1969)
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48:11 May 1942
823:Categories
765:2022-05-11
621:2022-05-11
590:2022-05-11
530:References
44:1942-05-11
661:-vectors.
522:115688843
411:122228607
317:122025424
247:Vancouver
182:g-theorem
782:Archived
732:: 6–12,
638:(1995),
478:(2002),
464:(1971),
442:(1993),
364:63778391
197:-vectors
746:0307040
695:2335496
514:1965665
447:1243000
435:0731112
403:1228132
383:Bibcode
356:0394436
336:Bibcode
309:0283691
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