Tag Archives: Richard Stanley

Cheerful news in difficult times: Richard Stanley wins the Steele Prize for lifetime achievement!

Richard Stanley, a most famous and influential mathematician in my area of combinatorics, the master of finding deep connections between combinatorics and other areas of pure mathematics, and my postdoctoral advisor, has just won the Steele prize for lifetime achievement, … Continue reading

Posted in Combinatorics | Tagged | 1 Comment

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 , , , , , , , , , , , , , , , , , , | 13 Comments

Happy Birthday Richard Stanley!

This week we are celebrating in Cambridge MA , and elsewhere in the world, Richard Stanley’s birthday.  For the last forty years, Richard has been one of the very few leading mathematicians in the area of combinatorics, and he found deep, profound, and … Continue reading

Posted in Combinatorics, Conferences, Happy birthday | Tagged | 6 Comments

Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found

The upper bound theorem asserts that among all d-dimensional polytopes with n vertices, the cyclic polytope maximizes the number of facets (and k-faces for every k). It was proved by McMullen for polytopes in 1970, and by Stanley for general triangulations … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , | 4 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

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

(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 , , , , , , , | 13 Comments