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Some constrained partitioning problems and majorization
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DOI：10.1016/S0377-2217(03)00256-X.png)
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Abstract
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We consider some constrained partitioning problems for a finite set of objects of different types. We look for partitions that are size- and type-similar, and, in addition, for a pair of such partitions that are very different in a certain sense. The motivation stems from a problem involving the partitioning of a set of students into smaller groups. We give these problems precise mathematical formulations and investigate these problems using the notion of majorization. A special case of one of the problems leads to a result concerning the packing of matchings in a bipartite graph. (C) 2003 Elsevier B.V. All rights reserved.
Keywords:
combinatorial optimization
partitioning
majorization
matching
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