Trees, Tight-Spans and Point Configuration

Details Trees, Tight-Spans and Point Configuration Trees, Tight-Spans and Point Configuration

2011-04-08

arxiv.org/abs/1104.1538v1

Mathematics

Combinatorics

20 pages

Scientific paper

Tight-spans of metrics were first introduced by Isbell in 1964 and rediscovered and studied by others, most notably by Dress who gave them this name. Subsequently, it was found that tight-spans could be defined for more general maps, such as directed metrics and distances, and more recently for diversities. In this paper, we show that all of these tight-spans can be defined in terms of point configurations. This provides a useful way in which to study these objects in a unified and systematic way. We also show that by using point configurations we can recover results concerning one-dimensional tight-spans for all of the maps we consider, as well as extend these and other results to more general maps such as symmetric and unsymmetric maps.

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