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Darf ich Zahlen?
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Darf ich Zahlen? Geschichten aus der Mathematik
Piper, Müchen ist als Hardcover im März 2010 erschienen; Taschenbuchpublikation Juni 2011.
Lesungen u.a.: München, Berlin, St. Augustin, Hannover, Berlin, Heilbronn, ...
Translations have appeared in
Korean (Dulnyouk),
Italian (Orme),
and
Czech (Universum).
Translations in Spanish (Destino) and Serbian (Center for Promotion of Science, Belgrade) are in preparation.
I in particular hope for a translation into English - sample chapter available.
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Pi & Co. - Kaleidoskop der Mathematik
Proofs from THE BOOK
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Proofs From THE BOOK
with Martin Aigner,
Springer-Verlag Heidelberg 1998;
(revised and
expanded) fourth edition, with five new chapters, 2009.
See the preface and the table of contents.
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Das BUCH der Beweise
mit Martin Aigner, Springer-Verlag Heidelberg 2001;
um fünf zusätzliche Kapitel erweiterte dritte deutsche Ausgabe, 2009;
hier sind Vorwort und Inhaltsverzeichnis.
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Raisonnements divins. Quelques demonstrations mathematiques particulièrement elegantes
with Martin Aigner (second edition of the French translation),
Springer-Verlag Paris, Paris 2006.
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Dowody z księgi
with Martin Aigner (Polish translation, by Paweł Strzelecki),
PWN Scientific Publishers, Warsaw 2002.
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As provas estão n'O LIVRO
with Martin Aigner (Portuguese/brazilian translation),
Editora Edgard Blücher, São Paulo 2002.
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Proofs from THE BOOK
with Martin Aigner (Japanese translation),
Springer-Verlag Tokyo, Tokyo 2002.
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Bizonyítások a Könyvből
with Martin Aigner (Hungarian translation, by Péter Komjáth),
Typotex Ltd., Budapest 2004.
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EL LIBRO de las demostraciones
with Martin Aigner (Spanish translation, by Lourdes Figueiras, Julian Pfeifle, and Edgar A. Ramos),
Nivola, Tres Cantos (Madrid), 2005.
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Proofs from THE BOOK. Edizione italiana a cura di Alfio Quarteroni
with Martin Aigner (Italian translation),
Springer, Milano, 2006.
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[Proofs from THE BOOK], Russian translation
by B. I. Selivanov and A. Zubkov, ISBN 5-03-003690-3,
Mir Scientific Publishers, Moscow, 2006.
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[Proofs from THE BOOK], Korean translation by M. Kang, Y. Koh, and S. Ree,
ISBN 978-89-8172-724-6, Kyowoosa Publisher,
Seoul, 2008.
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Kitap'tan Deliller [Proofs from THE BOOK], Turkish translation by A. Muhammed Uludag,
Bilgi Iletisim Grubu Yayincili, Sisli (Turkey), 2009.
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[Proofs from THE BOOK], Chinese translation by Chuanming Zong et al, Higher Education Press, Beijing 2009.
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... and there is also a Farsi translation by Siamak Kazemi,
IPM, Tehran, Iran, 2000.
Thus the book is now available in
fourteen different languages!
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Polytopes
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Face numbers of centrally symmetric polytopes from split graphs,
with
Ragnar Freij,
Matthias Henze, and
Moritz W. Schmitt,
Preprint, November 2011.
(arXiv:1201.5790)
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Inscribable stacked polytopes,
with Bernd Gonska,
Preprint, November 2011.
(arXiv:1109.5544)
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Many non-equivalent realizations of the associahedron,
with Cesar Ceballos
and Francesco Santos,
Preprint, September 2011.
(arXiv:1109.5544)
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A lost counterexample and a problem on illuminated polytopes,
with Ronald Wotzlaw,
American Math. Monthly 118 (2011), 534-543.
(arXiv:0908.1698)
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Zonotopes with large 2D cuts,
with Thilo Rörig
and Nikolaus Witte
Discrete & Comput. Geometry 42 (2009), 527-541.
(arXiv:0710.3116)
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Construction and analysis of projected deformed products,
with Raman Sanyal,
Discrete Comput. Geometry 43 (2010), 412-435
(arXiv:0710.2162)
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On Kalai's conjectures concerning centrally symmetric polytopes,
with Raman Sanyal
and Axel Werner,
Discrete Comput. Geometry 41 (2009), 183-198.
(arXiv:0708.3661)
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Euler's polyhedron formula as a starting point for
modern polytope theory,
with Christian Blatter,
Elemente der Math. 62 (2007), 184-192.
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AMS Steele Prize 2005:
Branko Grünbaum's
Convex Polytopes,
Second edition edited by
Volker Kaibel,
Victor Klee and
Günter M. Ziegler,
Graduate Texts in Mathematics 221,
Springer-Verlag
New York 2003.
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Projected products of polygons,
Electronic Research Announcements AMS,
10 (2004), 122-134
(arXiv:0407042)
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Convex Polytopes: Extremal constructions and f-vector shapes,
Park City Mathematical Institute (PCMI 2004) Lecture Notes. With an Appendix by
Thilo Schröder and
Nikolaus Witte (73 pages).
(arXiv:0411400)
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Construction techniques for cubical complexes, odd cubical 4-polytopes,
and prescribed dual manifolds,
with Alexander Schwartz,
Experimental Mathematics 13 (2004), 385-413 (arXiv:0310269)
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On the Monotone Upper Bound Problem,
with Julian Pfeifle,
Experimental Mathematics
13 (2004), 1-11 (arXiv:0308186)
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The Et-construction for lattices, spheres and polytopes,
with Andreas Paffenholz,
Discrete & Computational Geometry (Billera Festschrift);
32 (2004), 601-624 (arXiv:0304492)
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Many triangulated 3-spheres,
with Julian Pfeifle;
Math. Annalen 330 (2004), 829-837
(arXiv:0212004)
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Lectures on Polytopes
Graduate Texts in Mathematics 152,
Springer-Verlag
New York 1995, 370 pages; Revised sixth printing 2006.
Updates, Corrections, and More
available.
(Here
are the updates for the first printing; they
are obsolete with the second one.)
Japanese translation by Masahiro
Hachimori and Yoshio Okamoto
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Discrete Geometry
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Projecting lattice polytopes without interior lattice points,
with Benjamin Nill,
Mathematics of Operations Research 36 (2011), 462-467
(arXiv:1101.4292)
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Optimal elliptic Sobolev regularity near three--dimensional,
multi-material Neumann vertices,
with Robert Haller-Dintelmann, Wolfgang Höppner, Hans-Christoph Kaiser and Joachim Rehberg,
Matheon Preprint 808, April 2011, 27 pages.
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Polyhedral surfaces in wedge products,
with Thilo Rörig,
Geometriae Dedicata 151 (2011), 155-173,
(arXiv:0908.3159)
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On locally constructible spheres and balls
with Bruno Benedetti,
Acta Mathematica 206 (2011), 205-243.
(arXiv:0902.0436)
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Non-rational configurations, polytopes, and surfaces,
Mathematical Intelligencer, (3) 30 (2008), 36-42.
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Polyhedral surfaces of high genus,
in "Discrete Differential Geometry"
(Alexander I. Bobenko,
John M. Sullivan,
Peter Schröder, eds.),
Oberwolfach Seminars, Birkhäuser Basel, 2008
(arXiv:0412093)
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MAA Chauvenet Prize 2006:
Kissing numbers, sphere packings, and some unexpected proofs,
with Florian Pfender,
Notices of the AMS, September 2004, 873-883.
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Bier spheres and posets,
with Anders Björner,
Andreas Paffenholz, and
Jonas Sjöstrand,
Discrete & Computational Geometry 34 (2005), 71-86
(arXiv:0311356)
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Convex hulls, oracles, and homology,
with Michael Joswig,
J. Symbolic Computation (special issue for ICMS 2002) 38 (2004), 1247-1259;
(arXiv:0301100)
Combinatorics and Topological Methods
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3N Colored Points in a Plane,
Notices of the AMS, 58(4), April 2011, 550-557.
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A tight colored Tverberg theorem for maps to manifolds,
(with Pavle V. M. Blagojevic and Benjamin Matschke), Topology and its Applications (Proc. ATA2010),
158 (2011), 1445-1452. (arXiv:math.AT/1107.1904)
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Optimal bounds for a colorful Tverberg-Vrecica type problem,
(with Pavle V. M. Blagojevic and Benjamin Matschke),
Advances in Math. 226 (2011), 5198-5215.
(arXiv:math.AT/0911.2692)
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Optimal bounds for the colored Tverberg problem,
(with Pavle V. M. Blagojevic and Benjamin Matschke), Preprint, October 2009, 10 pages.
(arXiv:math.AT/0910.4987)
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Tetrahedra on deformed spheres and integral group cohomology,
(with Pavle V. M. Blagojevic), Electronic J. Combinatorics, Björner Festschrift,
Volume 16(2), 2009, R16.
(arXiv:math.AT/0808.3841)
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Combinatorial Stokes formulas via minimal resolutions,
with
Bernhard Hanke,
Raman Sanyal, and
Carsten Schultz,
J. Combinatorial Theory, Ser. A, 116 (2009), 404-420
(arXiv:0710.0050)
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The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes,
with Pavle V. M. Blagojevic, Preprint, TU Berlin, revised 3nd version, December 2010, 44 pages
(arXiv:0704.1943);
short version to appear in Topology and its Applications (Proceedings of ATA2010).
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On generalized Kneser hypergraph colorings,
with Carsten Lange,
J. Combinatorial Theory, Ser. A, 114 (2007), 159-166
(arXiv:0504607)
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The Topological Tverberg Theorem and winding numbers,
with Torsten Schöneborn,
J. Combinatorial Theory, Ser. A, 112 (2005), 82-104.
(arXiv:0409081)
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Jiri Matousek's
Using the Borsuk-Ulam Theorem. Lectures on Topological Methods in Combinatorics and Geometry,
(Written in collaboration with
Anders Björner and Günter M. Ziegler)
Universitext, Springer-Verlag Heidelberg, 2003.
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Singular 0/1-matrices, and the hyperplanes spanned by random 0/1-vectors,
with Thomas
Voigt
Combinatorics, Probability & Computing, 15 (2006), 463-471
(arXiv:0308050)
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Counting lattice triangulations,
with Volker Kaibel;
in "Surveys in Combinatorics 2003"
(C. D. Wensley, ed.), Proc. 19th British Combinatorial conference, June 29 - July 4, in Bangor/Wales, London Math. Society Lecture Notes Series, Vol. 307,
pp. 277-307, Cambridge University Press 2003 ---
(arXiv:0211268);
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Topological lower bounds for the chromatic number: A hierarchy,
with Jiri Matousek;
Jahresbericht der DMV 106 (2004), 71-90.
(arXiv:0208072)
Optimization
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