منابع مشابه
Linear Programming, the Simplex Algorithm and Simple Polytopes
In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
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For general polytopes, it has turned out that with respect to many questions it su ces to consider only the simple polytopes, i.e., d-dimensional polytopes where every vertex is contained in only d facets. In this paper, we show that the situation is very di erent within the class of 0/1-polytopes, since every simple 0/1-polytope is the (cartesian) product of some 0/1-simplices (which proves a ...
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We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P . We devise a combinatorial method to establish lower bounds on the simple extension complexity and show for several polytopes that they have large simple extension complexities. These example...
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P (h) φ(x)dx where the polytope P (h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of Khovanskii and Pukhlikov [8] (valid for lattice polytopes such that the primitive vectors on edges through each vertex of P form a basis of the lattice). As a corollary, we recover results of Pommersheim [9] and ...
متن کاملOn polytopes simple in edges
In this paper, we will study the h-vectors of a slightly more general class of polytopes. A d-polytope is called simple in edges if each its edge is incident exactly to d − 1 facets. We will prove that for any polytope simple in edges all numbers h[d/2], h[d/2]+1,. . ., hd are nonnegative and hk 6 hd−k for k 6 d/2. Polytopes simple in edges appear for instance as (closures of) fundamental polyh...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0328