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# Tag Archives: g-conjecture

## Amazing: Simpler and more general proofs for the g-theorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.

Stavros Argyrios Papadakis, Vasiliki Petrotou, and Karim Adiprasito In 2018, I reported here about Karim Adiprasito’s proof of the g-conjecture for simplicial spheres. This conjecture by McMullen from 1970 was considered a holy grail of algebraic combinatorics and it resisted … Continue reading

Posted in Algebra, Combinatorics, Geometry
Tagged g-conjecture, Hilda Geiringer, Karim Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
5 Comments

## Karim Adiprasito: The g-Conjecture for Vertex Decomposible Spheres

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 g-conjecture, J Scott Provan, Karim Adiprasito, Leonid Gurvits, Lou Billera
9 Comments

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

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

## 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
12 Comments

## 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
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 Lipton-Tarjan’s theorem extends to high … 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

## How the g-Conjecture Came About

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

## (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