{"created":"2023-05-15T15:12:28.977014+00:00","id":288,"links":{},"metadata":{"_buckets":{"deposit":"faa900d9-7c04-4d24-b32d-2a65ff1f1952"},"_deposit":{"created_by":16,"id":"288","owners":[16],"pid":{"revision_id":0,"type":"depid","value":"288"},"status":"published"},"_oai":{"id":"oai:ompu.repo.nii.ac.jp:00000288","sets":["87:88"]},"author_link":["530","532","533","534"],"control_number":"288","item_10002_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2022-03-28","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"45","bibliographicPageStart":"19","bibliographicVolumeNumber":"1","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":"In 2019, the authors of the current paper conducted a survey research on human-generated permutations [Nagata and Takei, Bull. OUPS 2019]. In the following year, they analyzed the data from\na different perspective and observed that people tend to generate certain types of permutations, then\ndefined types NAP (nearly arithmetic progression) and pNAP (pseudo-nearly arithmetic progression)\nof permutations as mathematical abstractions of such tendency [Nagata and Takei, Bull. OUPS 2020].\nThen, in [Nagata and Takei, Bull. OUPS 2021], the number of permutations of these types were bounded\nby asserting that the set of the inverse permutations of S´os type, which are defined as the translation\nof so-called S´os permutations [S´os, Ann. Univ. Sci. Budapest. E¨otv¨os, Sect. Math. 1958] by a constant,\ninclude the set of the permutations of NAP type and are included in the set of the permutations of\npNAP type. Especially, the authors obtained a lower bound of the number of the permutations of pNAP\ntype as the number of the permutations of S´os type whose explicit formula is obtained from the number\nof S´os permutations in [Sur´anyi, Ann. Univ. Sci. Budapest. E¨otv¨os, Sect. Math. 1958], [Shutov, Chebyshevskii Sb. 2014], [Bockiting-Conrad, Kashina, Petersen and Tenner, Amer. Math. Monthly 2021], with\nthe assertion by computer experiments that the set of the inverses of S´os type-permutations is indeed\nthe same as the set of the permutations of pNAP type as long as the degree n of the permutations is\nnot greater than 50. Thus, a remaining problem of major interest is bounding the number of pNAP\npermutations from above. In this paper, we address this problem. One of our results is that pNAP and\nthe inverses of S´os permutations satisfy essentially identical recurrence relation. It gives immediately an\nupper bound (n − 1)n2 of the number of permutations of pNAP type. We note that the upper bound is\nof the same order in n as the lower bound, the number of the inverses of S´os type-permutations. Furthermore, using the recurrence relation, an efficient algorithm for the enumeration of pNAP permutations\nis given and used to enlarge the upper limit of the degrees n for which the observed property “pNAP is\ninverse-S´os-type” is confirmed to 1300 from 50 in our previous paper.","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":"530","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"武井, 由智"},{"creatorName":"タケイ, ヨシノリ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"532","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"NAGATA, Makoto","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"533","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"TAKEI, Yoshinori","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"534","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":"2022-05-31"}],"displaytype":"detail","filename":"02_nagata.pdf","filesize":[{"value":"1.8 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"ある型の置換の個数について II","url":"https://ompu.repo.nii.ac.jp/record/288/files/02_nagata.pdf"},"version_id":"cdb03edd-cb7b-454b-af6d-8c73cd80206c"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"arithmetic progression","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"S´os permutation","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"symmetric group","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":"ある型の置換の個数についてII","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"ある型の置換の個数についてII","subitem_title_language":"ja"},{"subitem_title":"On the numbers of permutations of certain types II","subitem_title_language":"en"}]},"item_type_id":"10002","owner":"16","path":["88"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2022-05-31"},"publish_date":"2022-05-31","publish_status":"0","recid":"288","relation_version_is_last":true,"title":["ある型の置換の個数についてII"],"weko_creator_id":"16","weko_shared_id":-1},"updated":"2023-07-13T07:57:53.213572+00:00"}