Tag Archives: Polytopes

The Polynomial Hirsch Conjecture: Discussion Thread

This post is devoted to the polymath-proposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 115 Comments

The Polynomial Hirsch Conjecture: A proposal for Polymath3

This post is continued here.  Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a d-polytope with n vertices  facets has diameter at most n-d. We devoted several … Continue reading

Posted in Open problems, Convex polytopes, Open discussion | Tagged , , , | 38 Comments

How the g-Conjecture Came About

This post complements Eran Nevo’s first  post on the -conjecture 1) Euler’s theorem Euler Euler’s famous formula for the numbers of vertices, edges and faces of a  polytope in space is the starting point of many mathematical stories. (Descartes came close … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems | Tagged , , , , | 5 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 , , | 5 Comments

Combinatorics, Mathematics, Academics, Polemics, …

1. About: My name is Gil Kalai and I am a mathematician working mainly in the field of Combinatorics.  Within combinatorics, I work mainly on geometric combinatorics and the study of convex polytopes and related objects, and on the analysis of Boolean functions … Continue reading

Posted in Blogging, Combinatorics, Controversies and debates, Open problems | Tagged , , , , , , , , , , , | 13 Comments