منابع مشابه
A counterexample to the Hirsch conjecture
The Hirsch Conjecture (1957) stated that the graph of a d-dimensional polytope with n facets cannot have (combinatorial) diameter greater than n−d. That is, any two vertices of the polytope can be connected by a path of at most n− d edges. This paper presents the first counterexample to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope wit...
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متن کاملAn Approach to Hirsch Conjecture
W.M. Hirsch formulated a beautiful conjecture on amaximum of diameters of convex polyhedrawith both fixed dimension and number of facets. This is still unsolved for about 50 years. Here, I suggest a new method of argument from the viewpoint of deformation of polytope. As a candidate of the clue to the complete-proof, there’s some conjectures which are all sufficient for the original problem.
متن کاملAn Approach to the Hirsch Conjecture
W. M. Hirsch proposed a beautiful conjecture on diameters of convex polyhedra, which is still unsolved for about 50 years. I suggest a new method of argument from the viewpoint of deformation and moduli of polytopes. As a consequence, for example, if there are at least 3 disjoint geodisics for all Dantzig figures, as in the 3 dimensional case, the conjecture follows.
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By J onsson's Lemma, the variety V(K) generated by a nite lattice has only nitely many subvarieties. This led to the conjecture that, conversely, if a lattice variety has only nitely many subvarieties, then it is generated by a nite lattice. A stronger form of the conjecture states that a nitely generated variety V(K) has only nitely many covers in the lattice of lattice varieties, and that eac...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.176.1.7