Naslov
On volume-measure as hemi-metrics

Autori
Deza, Michel ; Dutour, Mathieu ; Maehara, Hiroshi

Izvornik
Ryukyu mathematical journal (1344-008X) 17 (2004); 1-9

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

Ključne riječi
hemi-metric ; cone ; extremal problem

Sažetak
Let m be a positive integer, and X be a point-set in a Euclidean space containing at least m+2 points. Let Mu be the map defined by Mu(x1, ..., x(m+1)) to be the m-dimensional volume of the convex hull of the point-set x1, ..., x(m+1). Denote by s(X, m) the maximal value of s such that the hemi-metric inequality holds. This s(X, m) is considered as bound of the m-simplex inequality. We prove that if x(X, 2)=3 and |X|>=5 then X is the vertex set of a regular simplex and present the value of s(X, m) of the vertex-sets of several convex polytopes. For the vertex-set of the n-dimensional octahedron, we have s(X, m)=3 for all n>=m>=3, while for the vertex set of the n-dimensional cube, we show s(X, m) converges to 1 as n goes to infinity for every m>0.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA