Naslov
Cones of metrics, hemi-metrics and super-metrics

Autori
Dutour, Mathieu ; Deza, Michel

Izvornik
Annals (European Academy of Sciences) (1784-0686) 1 (2003); 141-162

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
cone; hemi-metric; super-metric

Sažetak
A semi-metric is defined as a function d(x, y) satisfying d(x, x)=0, d(x, y)=d(y, x) and the triangle inequality d(x, z)<= d(x, y)+d(y, z). The set of all semi-metrics on n points form a polyhedral cone called metric cone. We consider here the m-hemi-metrics, which generalize m-dimensional volumes, and, more generally, the (m, s)-super-metrics and their corresponding cones. We present here some new data on related cones ; the number of facets, of extreme rays, of their orbits and diameters are collected in several tables. Examples of other results: (i) introduction of particular families of extreme rays of supermetric cones and of corresponding cones of generalized cuts, (ii) study of adjacencies of facets and of extreme rays in these cones, (iii) introduction of zero-extension and vertex-splitting operations on the extreme rays of hemi-metric cones.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA