2022-08-18T20:25:46Z https://u-ryukyu.repo.nii.ac.jp/oai
oai:u-ryukyu.repo.nii.ac.jp:02003573 2022-02-15T05:39:16Z 1642837622505:1642837628262:1642837636453 1642838403551:1642838406414
Inversions and Möbius invariants Maehara, Hiroshi 前原, 濶 open access 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 Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus eng departmental bulletin paper VoR http://hdl.handle.net/20.500.12000/4807 http://hdl.handle.net/20.500.12000/4807 https://u-ryukyu.repo.nii.ac.jp/records/2003573 1344-008X AA10779580 Ryukyu mathematical journal 20 9 23 https://u-ryukyu.repo.nii.ac.jp/record/2003573/files/Vol20p9.pdf