{"created":"2023-05-15T15:12:39.127774+00:00","id":517,"links":{},"metadata":{"_buckets":{"deposit":"e59643b9-62cb-4739-9102-8cc0e652df38"},"_deposit":{"created_by":16,"id":"517","owners":[16],"pid":{"revision_id":0,"type":"depid","value":"517"},"status":"published"},"_oai":{"id":"oai:ompu.repo.nii.ac.jp:00000517","sets":["87:152"]},"author_link":["1633","1632","1634","1631"],"item_10002_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2023-03-28","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"55","bibliographicPageStart":"21","bibliographicVolumeNumber":"2","bibliographic_titles":[{"bibliographic_title":"大阪医科薬科大学 薬学部雑誌"},{"bibliographic_title":"Bulletin of the Faculty of Pharmacy, Osaka Medical and Pharmaceutical University","bibliographic_titleLang":"en"}]}]},"item_10002_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"We consider a 2-dimensional version of Sur´anyi’s bijections for S´os permutations. Sur´anyi’s bijection\nis a bijective map between the set of the short intervals appearing as the division of the unit interval\nby the Farey sequence and the set of S´os permutations. A concept equivalent to Sur´anyi’s bijection\nis a bijective map between the set of the short intervals by the Farey sequence and the set of the\ninverses of S´os permutations. In this article, we attempt to give a 2-dimensional analogue of the latter\nmap. First, we introduce our 2D version, which we refer to as a ranking table, of the inverse of a S´os\npermutation. Then we define small polygons, which are bounded by the lines of so-called Farey diagram\nand some additional lines, as our 2D version of the short intervals by the Farey sequence. Based on\nthese definitions, we show that our map between the set of the small polygons and the set of the ranking\ntables is a well-defined surjection. Also, an examination using a computer shows that the map is in fact\nbijective, for all 81 cases (which can be reduced to 45 cases by a symmetry) which are chosen as the cases\nin which the size of the ranking table is small. Furthermore, we show that our map is indeed injective\nwhen the image of the map is restricted to the set of the ranking tables formed by the standard Young\ntableaux. This restricted map may be interpreted as yet another Sur´anyi’s bijection which is different\nfrom our 2D version. In fact, the domain which is similar to the short intervals by Farey sequences\nappears for our bijective map into the set of Young tableaux. We also mention the triangles-quadrangles\nconjecture for the Farey diagram in our context.","subitem_description_type":"Abstract"}]},"item_10002_publisher_8":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"大阪医科薬科大学薬学部"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"永田, 誠"},{"creatorName":"ナガタ, マコト","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"1631","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"武井, 由智"},{"creatorName":"タケイ, ヨシノリ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"1632","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"NAGATA, Makoto","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"1633","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"TAKEI, Yoshinori","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"1634","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2023-04-27"}],"displaytype":"detail","filename":"1-2_論文_永田誠・武井由智.pdf","filesize":[{"value":"1.3 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"1-2_論文_永田誠・武井由智","url":"https://ompu.repo.nii.ac.jp/record/517/files/1-2_論文_永田誠・武井由智.pdf"},"version_id":"83a906e7-29ea-4299-a1a0-47292e54445b"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Farey diagram","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Farey sequence","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"S´os permutation","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Sur´anyi’s bijection","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"symmetric group","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Young tableau","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"S´os 置換に関するSur´anyiの全単射のある2次元版について","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"S´os 置換に関するSur´anyiの全単射のある2次元版について"},{"subitem_title":"On a 2-dimensional version of Sur´anyi’s bijections for S´os permutations","subitem_title_language":"en"}]},"item_type_id":"10002","owner":"16","path":["152"],"pubdate":{"attribute_name":"公開日","attribute_value":"2023-05-01"},"publish_date":"2023-05-01","publish_status":"0","recid":"517","relation_version_is_last":true,"title":["S´os 置換に関するSur´anyiの全単射のある2次元版について"],"weko_creator_id":"16","weko_shared_id":-1},"updated":"2023-05-15T15:16:02.432682+00:00"}