{"created":"2022-01-27T07:38:03.868031+00:00","id":2003573,"links":{},"metadata":{"_buckets":{"deposit":"6940a59f-fb9b-41c1-a367-51923edef648"},"_deposit":{"id":"2003573","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2003573"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02003573","sets":["1642837622505:1642837628262:1642837636453","1642838403551:1642838406414"]},"author_link":[],"item_30002_access_rights4":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_30002_bibliographic_information29":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2007-12-30","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"23","bibliographicPageStart":"9","bibliographicVolumeNumber":"20"}]},"item_30002_creator2":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Maehara, Hiroshi","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"前原, 濶","creatorNameLang":"ja"}]}]},"item_30002_description9":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Other"},{"subitem_description":"紀要論文","subitem_description_type":"Other"}]},"item_30002_file35":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"Vol20p9.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2003573/files/Vol20p9.pdf"},"version_id":"36a8b121-3b48-4bf0-889d-0739efe61c6b"}]},"item_30002_identifier16":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/4807"}]},"item_30002_language12":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_30002_publisher10":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus","subitem_publisher_language":"en"}]},"item_30002_resource_type13":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_30002_source_identifier22":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_source_identifier":"1344-008X","subitem_source_identifier_type":"ISSN"},{"subitem_source_identifier":"AA10779580","subitem_source_identifier_type":"NCID"}]},"item_30002_source_title23":{"attribute_name":"Source Title","attribute_value_mlt":[{"subitem_source_title":"Ryukyu mathematical journal","subitem_source_title_language":"en"}]},"item_30002_title0":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_title":"Inversions and Möbius invariants","subitem_title_language":"ja"}]},"item_30002_version_type15":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_title":"Inversions and Möbius invariants","item_type_id":"30002","owner":"1","path":["1642837636453","1642838406414"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"2003573","relation_version_is_last":true,"title":["Inversions and Möbius invariants"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T01:24:54.090874+00:00"}