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References
- ↑ Peter McMullen, Peter M. Gruber, retrieved 2013-11-03.
- ↑ UCL IRIS information system, accessed 2013-11-05.
- ↑ McMullen, Peter; Schulte, Egon (12 December 2002), Abstract and regular polytopes, ISBN 9780521814966 , retrieved 2022-05-11
- ↑ Peter McMullen Collection, 1967-1968, Special Collections, Wilson Library, Western Washington University, retrieved from worldcat.org 2013-11-03.
- ↑ "Austrian Academy of Sciences: Peter McMullen" . Retrieved 2022-05-11.
- ↑ Ziegler, Günter M. (1995), Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152, Springer, p. 254, ISBN 9780387943657,
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 h-vectors.
- ↑ Gruber, Peter M. (2007), Convex and discrete geometry, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 336, Berlin: Springer, p. 265, ISBN 978-3-540-71132-2, MR 2335496,
The problem of characterizing the f-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 g-conjecture. The g-conjecture was proved by Billera and Lee and Stanley
. - ↑ Larman, D. G. (1972), "On sets projectively equivalent to the vertices of a convex polytope", The Bulletin of the London Mathematical Society, 4: 6–12, doi:10.1112/blms/4.1.6, MR 0307040
- ↑ "A picture of the E8 root system". American Institute of Mathematics. Retrieved 2022-05-11.
- ↑ ICM 1974 proceedings Archived 2017-12-04 at the Wayback Machine .
- ↑ Awards, Appointments, Elections & Honours, University College London, June 2006, retrieved 2013-11-03.
- ↑ List of AMS fellows, retrieved 2013-11-03.
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