Tag Archives: g-conjecture

Karim Adiprasito: The g-Conjecture for Vertex Decomposible Spheres

Posted on February 23, 2019 by

J Scott Provan (site) The following post was kindly contributed by Karim Adiprasito. (Here is the link to Karim’s paper.) Update: See Karim’s comment on the needed ideas for extend the proof to the general case. See also  in the … Continue reading →

Posted in Combinatorics, Convex polytopes, Geometry, Guest blogger | Tagged , , , , | 9 Comments

Amazing: Karim Adiprasito proved the g-conjecture for spheres!

Posted on December 25, 2018 by

Karim in his youth with a fan Congratulations, Karim! Update: Here is the link to the paper From the arXive, Dec 26, 2018. (Link will be added tomorrow.) COMBINATORIAL LEFSCHETZ THEOREMS BEYOND POSITIVITY by Karim Adiprasito Abstract: Consider a simplicial complex … Continue reading →

Posted in Combinatorics, Updates | Tagged , | 10 Comments

Beyond the g-conjecture – algebraic combinatorics of cellular spaces I

Posted on June 20, 2018 by

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 , , , , , , , , , , , , , , , , , , | 10 Comments

Eran Nevo: g-conjecture part 4, Generalizations and Special Cases

Posted on October 2, 2017 by

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 , | 2 Comments

Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies

Posted on October 28, 2015 by

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 →

Posted in Combinatorics, Convex polytopes | Tagged , , , , , | 3 Comments

(Eran Nevo) The g-Conjecture III: Algebraic Shifting

Posted on September 21, 2009 by

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 , , , , | 5 Comments

(Eran Nevo) The g-Conjecture II: The Commutative Algebra Connection

Posted on April 9, 2009 by

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 →

Posted in Combinatorics, Convex polytopes, Open problems | Tagged , , , , , | 9 Comments

How the g-Conjecture Came About

Posted on April 4, 2009 by

Update: Slides from a great 2014 lecture on the g-conjecture by Lou Billera in the conference celebrating Richard Stanley’s 70th birthday. This post complements Eran Nevo’s first  post on the -conjecture 1) Euler’s theorem Euler Euler’s famous formula for the … Continue reading →

Posted in Combinatorics, Convex polytopes, Open problems | Tagged , , , , | 14 Comments

(Eran Nevo) The g-Conjecture I

Posted on April 2, 2009 by

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 , , , , , , , | 12 Comments

Billerafest

Posted on June 12, 2008 by

I am unable to attend the conference taking place now at Cornell, but I send my warmest greetings to Lou from Jerusalem. The titles and abstracts of the lectures can be found here. Let me tell you about two theorems by Lou. … Continue reading →

Posted in Conferences, Convex polytopes | Tagged , , , | 1 Comment