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 Polymath10post 4: Back to the drawing board?
 News (mainly polymath related)
 Polymath 10 Post 3: How are we doing?
 Polymath10, Post 2: Homological Approach
 Polymath10: The Erdos Rado Delta System Conjecture
 Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies
 Igor Pak’s collection of combinatorics videos
 EDP Reflections and Celebrations
 Séminaire N. Bourbaki – Designs Exist (after Peter Keevash) – the paper
Top Posts & Pages
 Polymath 10 Post 3: How are we doing?
 Polymath10post 4: Back to the drawing board?
 Polymath10: The Erdos Rado Delta System Conjecture
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Believing that the Earth is Round When it Matters
 (Eran Nevo) The gConjecture I
 When It Rains It Pours
 News (mainly polymath related)
 Gödel, Hilbert and Brouwer
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Category Archives: Convex polytopes
Igor Pak’s “Lectures on Discrete and Polyhedral Geometry”
Here is a link to Igor Pak’s book on Discrete and Polyhedral Geometry (free download) . And here is just the table of contents. It is a wonderful book, full of gems, contains original look on many important directions, things that … Continue reading
Posted in Book review, Convex polytopes, Convexity
Tagged Convex polytopes, Convexity, Igor Pak, rigidity
4 Comments
The Polynomial Hirsch Conjecture: Discussion Thread
This post is devoted to the polymathproposal 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 Hirsch conjecture, Polytopes
115 Comments
The Polynomial Hirsch Conjecture – How to Improve the Upper Bounds.
I can see three main avenues toward making progress on the Polynomial Hirsch conjecture. One direction is trying to improve the upper bounds, for example, by looking at the current proof and trying to see if it is wasteful and if so where … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Discussion, Hirsch conjecture
14 Comments
The Polynomial Hirsch Conjecture, a Proposal for Polymath3 (Cont.)
The Abstract Polynomial Hirsch Conjecture A convex polytope is the convex hull of a finite set of points in a real vector space. A polytope can be described as the intersection of a finite number of closed halfspaces. Polytopes have … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Hirsch conjecture, Polymath proposals
5 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 dpolytope with n vertices facets has diameter at most nd. We devoted several … Continue reading
(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
How the gConjecture 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
(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 face rings, gconjecture, Polytopes
7 Comments
Ziegler´s Lecture on the Associahedron
The associahedron in 3 dimension, and James Stasheff. This picture is taken from Bill Casselman’s article on the associahedron. The article is entitled “Strange Associations” and starts with “There are many other polytopes that can be described in purely combinatorial terms. Among the … Continue reading
Posted in Convex polytopes
Tagged Associahedron, Cyclohedron, Permutahedron, Permutoassociahedron
7 Comments
Telling a Simple Polytope From its Graph
Peter Mani (a photograph by Emo Welzl) Simple polytopes, puzzles Micha A. Perles conjectured in the ’70s that the graph of a simple polytope determines the entire combinatorial structure of the polytope. This conjecture was proved in 1987 by Blind … Continue reading
Posted in Convex polytopes, Open problems
Tagged Eric Friedman, Peter Mani, Roswitta Blind
5 Comments