On The Number of Faces of a Convex Polytope

Author:

Gale David

Abstract

The following problem is as yet unsolved: Given a convex polytope with N vertices in n-space, what is the maximum number of (n — 1)-faces which it can have? Aside from its geometric interest this question arises in connection with solving systems of linear inequalities and linear equations in non-negative variables. The problem is equivalent to asking for the best bound on the number of basic solutions for such problems and hence a bound (though a weak one) for the number of iterations needed in the simplex method for solving linear programmes.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

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1. Bounds on the Number of Compatible k-Simplices Matching the Orientation of the (k − 1)-Skeleton of a Simplex;Combinatorica;2021-04

2. The Shifted Turán Sieve Method on Tournaments;Canadian Mathematical Bulletin;2019-04-11

3. Fast and robust algorithm to compute exact polytope parameter bounds;Mathematics and Computers in Simulation;1990-12

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