00 4 Classification of Six - Point Metrics
نویسنده
چکیده
There are 339 combinatorial types of generic metrics on six points. They correspond to the 339 regular triangulations of the second hypersimplex ∆(6, 2), which also has 14 non-regular triangulations. 1. The Metric Fan We consider the cone of all metrics on the finite set {1, 2, . . . , n}: Cn = { d ∈ R( n 2 ) : dij ≥ 0 and dij + djk ≥ dik for all 1 ≤ i, j, k ≤ n } . This is a closed convex pointed polyhedral cone. Its extreme rays have been studied in combinatorial optimization [4, 5]. Among the extreme rays are the splits. The splits are the metrics ∑
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