Branko Grünbaum is my academic grandfather (see this highly entertaining post for a picture representing five academic generations). Gunter Ziegler just wrote a beautiful article in the Notices of the AMS on Branko Grunbaum’s classic book “Convex Polytopes”, so this is an opportunity to tell the story of my copy. The book was written with the cooperation of Victor Klee, Micha Perles (my Ph. D supervisor) and Geoffrey Shephard. Since the late 70s the book was out of print and it was extremely difficult to get a copy.

In 1983 I was a postdoc in MIT and there was a lovely group of young combinatorialists around. At MIT, Noga Alon, and I, as well as Ian Goulden and a few others were postdocs, Jeff Kahn, Paul Seymour, Ira Gessel, and Anders Björner were junior faculty, Gunter Ziegler, Mark Haiman, Francesco Brenti, and Peter Shor were among the graduate students. There were many computer scientists with interest in combinatorics and at Northeastern there were two young faculty members, Marge Bayer and Dom (Dominique) de Caen working in combinatorics, and an algebraic geometer Jonathan Fine who also became interested in combinatorics.

One day, Dom de Caen saw me and told me that some months earlier he had managed to find a copy of “Convex polytopes” in a used book store and bought it for 10 dollars. He said that he knew how rare the book was and how hard it was to get it, but decided to give it to me since I would make better use of it working in this special area.

In 2003, after several years of work, a second edition was published which contained the original text and some additional material prepared by a fresh team of young researchers: Volker Kaibel, Victor Klee, and Gunter Ziegler. This was really great. I bought a copy and had the idea to send it to Dom as a form of gratitude for his previous gesture of kindness. So I tried to find his address over the Internet. I was sad to learn that Dom had passed away in 2002. You can read about Dom’s mathematics in this paper by Edwin R. Van Dam, The combinatorics of Dom de Caen.

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“and some additional material prepared by a fresh team of young researchers: […], Victor Klee, and […]” 😉

Dear Paco, I understand your skepticism: How can I refer to the team as a fresh team if Victor Klee was also on the original team? and how can I refer to it as a team of young researchers when Klee was the oldest member of both the first and the second teams? However, remebering Vic Klee, I feel that both these statements could be justified although I do not see yet precise formal proofs.

“I do not see yet precise formal proofs”. Maybe you can try to prove it undecidable.

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