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The number of faces of a simplicial convex polytope

✍ Scribed by Richard P Stanley


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
177 KB
Volume
35
Category
Article
ISSN
0001-8708

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Define the transportation polytope T n,m to be a polytope of non-negative n Γ— m matrices with row sums equal to m and column sums equal to n. We present a new recurrence relation for the numbers f k of the k-dimensional faces for the transportation polytope T n,n+1 . This gives an efficient algorith

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We prove two new upper bounds on the number of facets that a d-dimensional 0/1-polytope can have. The first one is 2(d -1)!+2(d -1) (which is the best one currently known for small dimensions), while the second one of O((d -2)!) is the best known bound for large dimensions.