@article{oai:u-ryukyu.repo.nii.ac.jp:02003573,
author = {Maehara, Hiroshi and 前原, 濶},
journal = {Ryukyu mathematical journal},
month = {Dec},
note = {Two $n$-point-sets in Euclidean space are said to be inversion-equivalent if one set can be transformed into the other set by applying inversions of the space. All 3-point-sets are inversion-equivalent to each other. For each four points $x,y,z,w$ in an $n$-point-set, $n\ge 4$, the ratio $\left( xy \cdot zw \right)$/$\left( xw \cdot yz \right)$ is invariant under inversions, which is called a Möbius invariant of the $n$-point-set. We prove that for $4\le n\le d+2$, the minimum number of Möbius invariants necessary to detetmine all Möbius invariants for every $n$-point-set in Euclidean $d$-space is equal to $n(n-3)/2$, and discuss the case of planar $n$-point-sets in some detail. We also characterize those fractional functions that are invariant under inversions., 紀要論文},
pages = {9--23},
title = {Inversions and Möbius invariants},
volume = {20},
year = {2007}
}