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IMI/Publicaţii/CSJM/Ediţii/CSJM v.15, n.3 (45), 2007/

Minimum convex partitions of multidimensional polyhedrons

Authors: Ion Băţ
Keywords: Geometric n-dimensional polyhedron, d-convexity, point of local non-d-convexity, polyhedral complex, oriented polytope, dividing.

Abstract

In a normed space Rn over the field of real numbers ℜ, which is an α-space [26, 29], one derives the formula expressing the minimum number of d-convex pieces into which a geometric n-dimensional polyhedron can be partitioned. The mentioned problem has been kept unsolvable for more than 30 years. The special cases for R2 , R3 lead to nontrivial applications [19, 20, 23, 28, 30].
Mathematics Subject Classification: 68U05, 52A30, 57Q05

Ion Băţ
Faculty of Mathematics and Computer Science
Moldova State University, MD-2009 Chisinau
Republic of Moldova
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