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Tag Archives: Eran Nevo
Beyond the gconjecture – algebraic combinatorics of cellular spaces I
The gconjecture 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, gconjecture, Günter Ziegler, Isabella Novik, June Huh, Kalle Karu, Karim Adiprasito, KazhdanLustig polynomials, Lou Billera, Marge Bayer, Peter McMullen, Richard Stanley, Ron Adin, Satoshi Murai, Tom Braden
14 Comments
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
2 Comments
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
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
1 Comment
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 gConjecture III: Algebraic Shifting
This is the third 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. … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged algebraic shifting, Eran Nevo, gconjecture, Karanbir Sarkaria, Shifting
5 Comments
(Eran Nevo) The gConjecture 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 gconjecture: 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 gConjecture I
This post is authored by Eran Nevo. (It is the first in a series of five posts.) Peter McMullen The gconjecture What are the possible face numbers of triangulations of spheres? There is only one zerodimensional sphere and it consists … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged Carl Lee, Eran Nevo, face rings, gconjecture, Lou Billera, Peter McMullen, Polytopes, Richard Stanley
13 Comments