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 My Very First Book “Gina Says”, Now Published by “World Scientific”
 Itai Benjamini: Coarse Uniformization and Percolation & A Paper by Itai and me in Honor of Lucio Russo
 AfterDinner Speech for Alex Lubotzky
 Boaz Barak: The different forms of quantum computing skepticism
 Bálint Virág: Random matrices for Russ
 Test Your Intuition 33: The Great Free Will Poll
 Mustread book by Avi Wigderson
 High Dimensional Combinatorics at the IIAS – Program Starts this Week; My course on Hellytype theorems; A workshop in Sde Boker
 Stan Wagon, TYI 23: Ladies and Gentlemen: The Answer
Top Posts & Pages
 My Very First Book "Gina Says", Now Published by "World Scientific"
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 TYI 30: Expected number of Dice throws
 Test Your Intuition 33: The Great Free Will Poll
 Believing that the Earth is Round When it Matters
 If Quantum Computers are not Possible Why are Classical Computers Possible?
 Can Category Theory Serve as the Foundation of Mathematics?
 Itai Benjamini: Coarse Uniformization and Percolation & A Paper by Itai and me in Honor of Lucio Russo
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Category Archives: Convex polytopes
Eran Nevo: gconjecture part 4, Generalizations and Special Cases
This is the fourth in a series of posts by Eran Nevo on the gconjecture. Eran’s first post was devoted to the combinatorics of the gconjecture and was followed by a further post by me on the origin of the gconjecture. Eran’s second post was about … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged Eran Nevo, gconjecture
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Touching Simplices and Polytopes: Perles’ argument
Joseph Zaks (1984), picture taken by Ludwig Danzer (OberWolfach photo collection) The story I am going to tell here was told in several places, but it might be new to some readers and I will mention my own angle, … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Joseph Zaks, Micha A. Perles
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Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies
I am happy to report on two beautiful results on convex polytopes. One disproves an old conjecture of mine and one proves an old conjecture of mine. Loiskekoski and Ziegler: Simple polytopes without small separators. Does LiptonTarjan’s theorem extends to high … Continue reading
The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
A quick schematic roadmap to these new geometric objects. The positroidron can be seen as a cellular structure on the nonnegative Grassmanian – the part of the real Grassmanian G(m,n) which corresponds to m by n matrices with all m by … Continue reading
My Mathematical Dialogue with Jürgen Eckhoff
Jürgen Eckhoff, Ascona 1999 Jürgen Eckhoff is a German mathematician working in the areas of convexity and combinatorics. Our mathematical paths have met a remarkable number of times. We also met quite a few times in person since our first … Continue reading
Posted in Combinatorics, Convex polytopes, Open problems
Tagged Andy Frohmader, Helly's theorem, Jurgen Eckhoff, Nina Amenta, Noga Alon, Roy Meshulam
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Many triangulated threespheres!
The news Eran Nevo and Stedman Wilson have constructed triangulations with n vertices of the 3dimensional sphere! This settled an old problem which stood open for several decades. Here is a link to their paper How many nvertex triangulations does the 3 … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Eran Nevo, Stedman Wilson
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Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found
The upper bound theorem asserts that among all ddimensional polytopes with n vertices, the cyclic polytope maximizes the number of facets (and kfaces for every k). It was proved by McMullen for polytopes in 1970, and by Stanley for general triangulations … Continue reading
Lionel Pournin found a combinatorial proof for SleatorTarjanThurston diameter result
I just saw in Claire Mathieu’s blog “A CS professor blog” that a simple proof of the SleatorTarjanThurston’s diameter result for the graph of the associahedron was found by Lionel Pournin! Here are slides of his lecture “The diameters of associahedra” … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Convex polytopes
Tagged Associahedron, Lionel Pournin
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Karim Adiprasito: Flag simplicial complexes and the nonrevisiting path conjecture
This post is authored by Karim Adiprasito The past months have seen some exciting progress on diameter bounds for polytopes and polytopal complexes, both in the negative and in the positive direction. Jesus de Loera and Steve Klee described simplicial polytopes which are not … Continue reading
Posted in Convex polytopes, Guest blogger
Tagged Convex polytopes, Flag complexes, Hirsch conjecture, Karim Adiprasito
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