TY - JOUR
T1 - Partition polytopes over 1-dimensional points
AU - Gao, Biao
AU - Hwang, Frank K.
AU - Li, Wen Ching Winnie
AU - Rothblum, Uriel G.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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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U2 - 10.1007/s101070050060
DO - 10.1007/s101070050060
M3 - Article
AN - SCOPUS:0347362946
SN - 0025-5610
VL - 85
SP - 335
EP - 362
JO - Mathematical Programming, Series B
JF - Mathematical Programming, Series B
IS - 2
ER -