Partition polytopes over 1-dimensional points

Partition polytopes over 1-dimensional points

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Article ID: iaor20001773
Country: Germany
Volume: 85
Issue: 2
Start Page Number: 335
End Page Number: 362
Publication Date: Jan 1999
Journal: Mathematical Programming
Authors: , , ,
Keywords: sets
Abstract:

We consider partitions of a finite set whose elements are associated with a single numerical attribute. For each partition we consider the vector obtained by taking the sums of the attributes corresponding to the elements in the parts (sets) of the partition, and we study the convex hulls of sets of such vectors. For sets of all partitions with prescribed number of elements in each set, we obtain a characterizing system of linear inequalities and an isomorphic representation of the face lattice. The relationship of the resulting class of polytopes to that of generalized permutahedra is explored.

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