An Introduction to Convex Polytopes

@inproceedings{Brndsted1982AnIT,
  title={An Introduction to Convex Polytopes},
  author={Arne Br{\o}ndsted},
  year={1982}
}
1 Convex Sets.- 1. The Affine Structure of ?d.- 2. Convex Sets.- 3. The Relative Interior of a Convex Set.- 4. Supporting Hyperplanes and Halfspaces.- 5. The Facial Structure of a Closed Convex Set.- 6. Polarity.- 2 Convex Polytopes.- 7. Polytopes.- 8. Polyhedral Sets.- 9. Polarity of Polytopes and Polyhedral Sets.- 10. Equivalence and Duality of Polytopes.- 11. Vertex-Figures.- 12. Simple and Simplicial Polytopes.- 13. Cyclic Polytopes.- 14. Neighbourly Polytopes.- 15. The Graph of a Polytope… 
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References

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1* Definitions and preliminary results* If v is a vertex of a d-polytope P then the antistar of v in P, denoted ast(v, P), is the set of all ά-faces of P that miss v, 0 <Ξ k ̂ d — 1. If H is a
Polytope pairs and their relationship to linear programming
Abstract : An important development in the theory of (convex) polytopes was the determination by Barnette and McMullen of the minimum and maximum of v(P) (number of vertices of P) as P ranges over
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For convex d-polytope P let ft{P) equal the number of faces of P of dimension i, 0 < i < d 1. f(P) = (f0(P)9 . . . , fd^QP)) is called the f vector of P An important combinatorial problem is the
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for some k, 0 < k < n. Empirical evidence has suggested that some important numerical sequences in combinatorics are unimodal. For instance, unimodality conjectures have been made for the
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Ad-polytope is ad-dimensional set that is the convex hull of a finite number of points. Ad-polytope is simple provided each vertex meets exactlyd edges. It has been conjectured that for simple
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In this paper we give a proof of the long-standing Upper-bound Conjecture for convex polytopes, which states that, for 1 ≤ j d v , the maximum possible number of j -faces of a d -polytope with v
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In this paper is considered the problem of determining the possiblef-vectors of simplicial polytopes. A conjecture is made about the form of the sclution to this problem; it is proved in the case
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