@article{oai:ynu.repo.nii.ac.jp:00007021,
 author = {Maehara, Hiroshi and Ueda, Sumie},
 issue = {2},
 journal = {Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学},
 month = {},
 note = {application/pdf, For two distinct points ＄P,＄ ＄Q＄ in the plane, let ＄Q^{P}＄ denote the point on the ray ＄￥overline{PQ}＄ such that ＄PQ￥cdot PQ^{P}=1＄ , and let ＄P^{P}=P＄. For a point-set ＄￥tau＄ in the plane and ＄ P￥in￥tau＄ , define ＄￥tau^{P}=￥{Q^{P}|Q￥in￥tau￥}＄ . The transformation ＄￥tau￥rightarrow￥tau^{P}＄ is called the pivotal inversion at ＄ P￥in￥tau＄ . We show that if ＄n￥geq 4＄ then starting from any n-point-set, it is possible, by applying a sequence of pivotal inversions, to produce an n-point-set whose diameter exceeds any prescribed value, but it is impossible to produce more than ＄n+1＄ mutually non-similar ＄n-point-sets＄ . The latter part is proved by showing a group induced by pivotal inversions of ordered ＄n-point＄-sets is isomorphic to the symmetric group of degree ＄n+1＄ .},
 pages = {119--126},
 title = {PIVOTAL INVERSIONS OF A FINITE POINT-SET},
 volume = {53},
 year = {2007}
}