5 papers
Excess inertia of finite metric spaces
Kiyonori Gomi
This paper classifies the possible inertias that are realized by an excess matrix of a finite metric space with at most nine points. For the classification, we make use of relation…
On the monotonicity of magnitude functions of negative type finite semimetric spaces
Kiyonori Gomi, Hiroshi Tsuji
Motivated by the conjectured monotonicity of the magnitude functions of metric spaces of negative type, we investigate the monotonicity problem for finite semimetric spaces, namely…
Geometric interpretation of magnitude
Yasuhiko Asao, Kiyonori Gomi
For an positive definite symmetric matrix with for all , we show that there exists a set of vectors such that the radius $…
Magnitude and matrix inequalities
Kiyonori Gomi, Mark Meckes
We present several applications of matrix-theoretic inequalities to the magnitude of metric spaces. We first resolve an open problem by showing that the magnitude of any finite met…
A direct proof for the positive definiteness of four point metric spaces
Kiyonori Gomi
We provide a direct and elementary proof for the fact that every four point metric space is positive definite, which was first proved by Meckes based on some embedding theorems of…