{"created":"2025-01-19T01:45:04.332114+00:00","updated":"2025-01-19T07:53:19.604072+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00240723","sets":["6164:6165:6210:11853"]},"path":["11853"],"owner":"44499","recid":"240723","title":["一般化されたヨセフスの問題と Maxニム"],"pubdate":{"attribute_name":"公開日","attribute_value":"2024-11-15"},"_buckets":{"deposit":"3e841139-1697-418e-a915-f30e9f49f527"},"_deposit":{"id":"240723","pid":{"type":"depid","value":"240723","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"一般化されたヨセフスの問題と Maxニム","author_link":["660898","660896","660899","660901","660903","660902","660897","660900"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"一般化されたヨセフスの問題と Maxニム"},{"subitem_title":"Generalized Josephus problem and maximum nim","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"ヨセフスの問題","subitem_subject_scheme":"Other"},{"subitem_subject":"Max ニム","subitem_subject_scheme":"Other"},{"subitem_subject":"グランディ数","subitem_subject_scheme":"Other"},{"subitem_subject":"組合せゲーム理論","subitem_subject_scheme":"Other"},{"subitem_subject":"不偏ゲーム","subitem_subject_scheme":"Other"}]},"item_type_id":"18","publish_date":"2024-11-15","item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_18_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"啓明学院高等学校"},{"subitem_text_value":"啓明学院高等学校"},{"subitem_text_value":"早稲田大学"},{"subitem_text_value":"慶應義塾大学"}]},"item_18_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Keimei Gakuin Junior and Senior High School","subitem_text_language":"en"},{"subitem_text_value":"Keimei Gakuin Junior and Senior High School","subitem_text_language":"en"},{"subitem_text_value":"Waseda University","subitem_text_language":"en"},{"subitem_text_value":"Faculty of Environment and Information Studies, Keio University","subitem_text_language":"en"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/240723/files/IPSJ-GPWS2024005.pdf","label":"IPSJ-GPWS2024005.pdf"},"date":[{"dateType":"Available","dateValue":"2024-11-15"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-GPWS2024005.pdf","filesize":[{"value":"255.1 kB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"0","billingrole":"5"},{"tax":["include_tax"],"price":"0","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"18"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"57ed1176-adb0-4d72-81fa-e0d17db8313a","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2024 by the Information Processing Society of Japan"}]},"item_18_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"眞部, 光"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"宮寺, 良平"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"末續, 鴻輝"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"高橋, 祥英"}],"nameIdentifiers":[{}]}]},"item_18_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Hikaru, Manabe","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Ryohei, Miyadera","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Koki, Suetsugu","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Shoei, Takahashi","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_5794","resourcetype":"conference paper"}]},"item_18_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"ヨセフスの問題は,古くから知られている数学の問題であり,円形に並んだ n 人の人間を,起点からk 人目を順に消していき,最後に生き残るのはどの人間かを求めるものである.また, Max ニムは組合せゲーム理論で扱われるゲームの中で特に不偏ゲームに属するゲームであり,局面として石の山と関数 f(本稿では制約関数と呼ぶ)が与えられ、それぞれの手番でその時点での山の石の総数 x に対して高々 f(x)個まで石を取り合い,着手ができなくなった方が負けとなるゲームである.これまで, f(x) = ⌊x/k ⌋ となる関数によって定義される Max ニムのグランディ数と k 人目を消していくヨセフスの問題の関係が知られていた.本研究ではこの対応関係を一般化し,飛ばす人数が一定でないヨセフスの問題に対しても対応する Max ニムが定義できること,並びに任意の広義単調増加な制約関数で定義される Max ニムに対して,対応するヨセフスの問題の飛ばし人数順が存在することを示し,さらに具体的な構成方法も示す.","subitem_description_type":"Other"}]},"item_18_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"Josephus problem is an old problem in mathematics: there are n persons in a circle, we start from a person and continue to remove every k-th person until only one person survives, then, how we can find the survivor from the initiate position? Also, max nim is a combinatorial game, which is impartial. In this ruleset, a pile of stones is given as a position and also restrict function f is given. The current player can remove at most f(x) stones, where x is the number of stones in the pile. The player who cannot make a move is the loser. So far, a relationship between max nim defined by f(x) = ⌊x/k⌋ and Josephus problem in which every k-th person is removed has already shown. In this study, we generalize this relationship and show that we can define restrict function for max nim corresponds to a Josephus problem in which the number of skipped person is not a constant, and we can define the sequence of skipped persons of the Josephus problem corresponding to the max nim defined by given weakly increasing function. We show a concrete method to obtain such restricted function and sequence of skipped persons.","subitem_description_type":"Other"}]},"item_18_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"39","bibliographic_titles":[{"bibliographic_title":"ゲームプログラミングワークショップ2024論文集"}],"bibliographicPageStart":"32","bibliographicIssueDates":{"bibliographicIssueDate":"2024-11-15","bibliographicIssueDateType":"Issued"},"bibliographicVolumeNumber":"2024"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":240723,"links":{}}