Article

# Equilateral Dimension of the Rectilinear Space.

(Impact Factor: 0.73). 01/2000; 21:149-164. DOI: 10.1023/A:1008391712305
Source: CiteSeer

ABSTRACT It is conjectured that there exist at most 2k equidistant points in the k- dimensional rectilinear space. This conjecture has been verified for k 3; we show here its validity in dimension k = 4. We also discuss a number of related questions. For instance, what is the maximum number of equidistant points lying in the hyperplane: P k i=1 x i = 0 ? If this number would be equal to k, then the above conjecture would follow. We show, however, that this number is k + 1 for k 4. 1

0 Followers
·
60 Views
• Source
##### Article: The 22 minimal dichotomy decompositions of the K5-distance
[Hide abstract]
ABSTRACT: In this note, we exhibit the 22 minimal dichotomy decompositions of the K5-distance.The proof of exhaustivity is simple and relatively short. A simple checking of the solutions gives an immediate validation of two conjectures concerning the dimensionality (known result for five points) and principal component analysis (unknown result).
Discrete Applied Mathematics 04/2008; 156(8):1263-1270. DOI:10.1016/j.dam.2007.05.026 · 0.68 Impact Factor
• Source
##### Article: Variations of a combinatorial problem on finite sets
[Hide abstract]
ABSTRACT: This interesting introductory paper surveys three equivalent reformulations of a possible Fisher type inequality for multisets.
Elemente der Mathematik 01/2007; DOI:10.4171/EM/55
• ##### Article: EMBEDDING METRIC SPACES INTO NORMED SPACES
[Hide abstract]
ABSTRACT: Let Md be an arbitrary real normed space of finite dimension d ‚ 2. We define the metric capacity of Md as the maximal m 2 N such that every m-point metric space is isometric to some subset of Md (with metric induced by Md). We obtain that the metric capacity of Md lies in the range from 3 to ¥3 2d ƒ + 1, where the lower bound is sharp for all d, and the upper bound is shown to be sharp for d 2 {2,3}. Thus, the unknown sharp upper bound is asymptotically linear, since it lies in the range from d + 2 to ¥3 2d ƒ + 1.