On The Number of Faces of a Convex Polytope
1964 ◽
Vol 16
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pp. 12-17
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Keyword(s):
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.
Keyword(s):
1964 ◽
Vol 16
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pp. 701-720
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Keyword(s):
1933 ◽
Vol 35
(2)
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pp. 452-452
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1985 ◽
Vol 65
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pp. 45-62
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Keyword(s):