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Tag Archives: Eran Nevo
Beyond the g-conjecture – algebraic combinatorics of cellular spaces I
The g-conjecture for spheres is surely the one single conjecture I worked on more than on any other, and also here on the blog we had a sequence of posts about it by Eran Nevo (I,II,III,IV). Here is a great … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry
Tagged Anders Bjorner, Bob MacPherson, Carl Lee, Ed Swartz, Eran Nevo, g-conjecture, Günter Ziegler, Isabella Novik, June Huh, Kalle Karu, Karim Adiprasito, Kazhdan-Lustig polynomials, Lou Billera, Marge Bayer, Peter McMullen, Richard Stanley, Ron Adin, Satoshi Murai, Tom Braden
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Eran Nevo: g-conjecture part 4, Generalizations and Special Cases
This is the fourth in a series of posts by Eran Nevo on the g-conjecture. Eran’s first post was devoted to the combinatorics of the g-conjecture and was followed by a further post by me on the origin of the g-conjecture. Eran’s second post was about … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged Eran Nevo, g-conjecture
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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 Lipton-Tarjan’s theorem extends to high … Continue reading
Many triangulated three-spheres!
The news Eran Nevo and Stedman Wilson have constructed triangulations with n vertices of the 3-dimensional sphere! This settled an old problem which stood open for several decades. Here is a link to their paper How many n-vertex triangulations does the 3 … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Eran Nevo, Stedman Wilson
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Satoshi Murai and Eran Nevo proved the Generalized Lower Bound Conjecture.
Satoshi Murai and Eran Nevo have just proved the 1971 generalized lower bound conjecture of McMullen and Walkup, in their paper On the generalized lower bound conjecture for polytopes and spheres . Let me tell you a little about it. … Continue reading
(Eran Nevo) The g-Conjecture III: Algebraic Shifting
This is the third in a series of posts by Eran Nevo on the g-conjecture. Eran’s first post was devoted to the combinatorics of the g-conjecture and was followed by a further post by me on the origin of the g-conjecture. … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged algebraic shifting, Eran Nevo, g-conjecture, Karanbir Sarkaria, Shifting
5 Comments
(Eran Nevo) The g-Conjecture II: The Commutative Algebra Connection
Richard Stanley This post is authored by Eran Nevo. (It is the second in a series of five posts.) The g-conjecture: the commutative algebra connection Let be a triangulation of a -dimensional sphere. Stanley’s idea was to associate with a ring … Continue reading
(Eran Nevo) The g-Conjecture I
This post is authored by Eran Nevo. (It is the first in a series of five posts.) Peter McMullen The g-conjecture What are the possible face numbers of triangulations of spheres? There is only one zero-dimensional sphere and it consists … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged Carl Lee, Eran Nevo, face rings, g-conjecture, Lou Billera, Peter McMullen, Polytopes, Richard Stanley
13 Comments
Combinatorics and more 