Counting disjoint 2-partitions for points in the plane

Authors:
F. H. Chang;J. Y. Guo;F. K. Hwang;J. S. Lee
Affiliations:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan, ROC
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

Disjoint partitions, and its counting, have been widely studied in the literature of optimal partitions and clustering. We give an exact counting on the number of disjoint ordered 2-partitions for n points in general position in . We also give an exact counting on the maximum number of disjoint 2-partitions, where one part consists of two points, over all sets of n points in .