{"created":"2025-02-21T03:37:35.964104+00:00","id":2006976,"links":{},"metadata":{"_buckets":{"deposit":"0cc54673-7062-46ac-b594-c431994ba0ad"},"_deposit":{"created_by":41,"id":"2006976","owners":[41],"pid":{"revision_id":0,"type":"depid","value":"2006976"},"status":"published"},"_oai":{"id":"oai:hiroshima.repo.nii.ac.jp:02006976","sets":["1730444907710"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_title":"Counting the number of bounded domains separated by hyperplanes","subitem_title_language":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Imaoka, Mitsunori","creatorNameLang":"en"}],"familyNames":[{"familyName":"Imaoka","familyNameLang":"en"}],"givenNames":[{"givenName":"Mitsunori","givenNameLang":"en"}]}]},"item_1617186476635":{"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_1617186609386":{"attribute_name":"Subject","attribute_value_mlt":[{"subitem_subject":"370","subitem_subject_scheme":"NDC"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"When some hyperplanes H_1, ..., H_m of the n-dimensional Euclidean space R^n are given in general position, Schläfli has determined the number of the bounded connected components in R^n - ∪^m_i = _1H_i, the complementary set of the union of the hyperplanes. It is equal to the binomial coefficient ((m-1)/n), which is also equal to the number of vertices which are the intersections of n hyperplanes in H_1, ..., H_<m-1>. Although Schläfli's proof is implicit and intuitive, the fact reflects an interesting aspect concerning configurations of hyperplanes. We clarify how the condition of general position works, and re-prove the fact in all of its details.","subitem_description_language":"en"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"Department of Mathematics Education, Faculty of Education, Hiroshima University"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_source_identifier":"0919-1720","subitem_source_identifier_type":"ISSN"},{"subitem_source_identifier":"AN10444573","subitem_source_identifier_type":"NCID"}]},"item_1617187024783":{"attribute_name":"Page Start","attribute_value_mlt":[{"subitem_start_page":"55"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1999-03","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"62","bibliographicPageStart":"55","bibliographicVolumeNumber":"7","bibliographic_titles":[{"bibliographic_title":"Hiroshima journal of mathematics education"},{"bibliographic_title":"Hiroshima journal of mathematics education"}]}]},"item_1617258105262":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_1617265215918":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","date":[{"dateType":"Available","dateValue":"2023-03-18"}],"displaytype":"simple","filename":"HiroshimaJMathEduc_7_55.pdf","filesize":[{"value":"441.5 KB"}],"mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://hiroshima.repo.nii.ac.jp/record/2006976/files/HiroshimaJMathEduc_7_55.pdf"},"version_id":"5887f63c-ef0c-4d7a-b7f5-5a2692787050"}]},"item_1732771732025":{"attribute_name":"旧ID","attribute_value":"29289"},"item_title":"Counting the number of bounded domains separated by hyperplanes","item_type_id":"40003","owner":"41","path":["1730444907710"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2023-03-18"},"publish_date":"2023-03-18","publish_status":"0","recid":"2006976","relation_version_is_last":true,"title":["Counting the number of bounded domains separated by hyperplanes"],"weko_creator_id":"41","weko_shared_id":-1},"updated":"2025-02-21T08:52:56.250119+00:00"}