An Approach to Hirsch Conjecture
نویسنده
چکیده
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.
منابع مشابه
An 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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