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Enumeration of Associative Magic Squares of Order 7
https://ipsj.ixsq.nii.ac.jp/records/208831
https://ipsj.ixsq.nii.ac.jp/records/2088315740935f-a046-412a-82d1-d9b9b5521980
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
IPSJ-JNL6112021.pdf (668.5 kB)
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Copyright (c) 2020 by the Information Processing Society of Japan
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| オープンアクセス | ||
| Item type | Journal(1) | |||||||||
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| 公開日 | 2020-12-15 | |||||||||
| タイトル | ||||||||||
| タイトル | Enumeration of Associative Magic Squares of Order 7 | |||||||||
| タイトル | ||||||||||
| 言語 | en | |||||||||
| タイトル | Enumeration of Associative Magic Squares of Order 7 | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| キーワード | ||||||||||
| 主題Scheme | Other | |||||||||
| 主題 | [特集：離散と計算の幾何・グラフ・ゲーム] magic squares, associative magic squares, enumeration | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | journal article | |||||||||
| 著者所属 | ||||||||||
| Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University | ||||||||||
| 著者所属 | ||||||||||
| Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University | ||||||||||
| 著者所属(英) | ||||||||||
| en | ||||||||||
| Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University | ||||||||||
| 著者所属(英) | ||||||||||
| en | ||||||||||
| Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University | ||||||||||
| 著者名 |
Go, Kato
× Go, Kato
× Shin-ichi, Minato
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| 著者名(英) |
Go, Kato
× Go, Kato
× Shin-ichi, Minato
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| 論文抄録 | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | An associative magic square is a magic square such that the sum of any 2 cells at symmetric positions with respect to the center is constant. The total number of associative magic squares of order 7 is enormous and thus, it is not realistic to obtain the number by simple backtracking. As a recent result, Ripatti reported the number of semi-magic squares of order 6 (the magic squares of 6 × 6 without diagonal sum conditions) in 2018. In this research, with reference to Ripatti's method of enumerating semi-magic squares, we have calculated the total number of associative magic squares of order 7. There are exactly 1,125,154,039,419,854,784 associative magic squares of order 7 excluding symmetric patterns. ------------------------------ This is a preprint of an article intended for publication Journal of Information Processing(JIP). This preprint should not be cited. This article should be cited as: Journal of Information Processing Vol.28(2020) (online) DOI http://dx.doi.org/10.2197/ipsjjip.28.903 ------------------------------ |
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| 論文抄録(英) | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | An associative magic square is a magic square such that the sum of any 2 cells at symmetric positions with respect to the center is constant. The total number of associative magic squares of order 7 is enormous and thus, it is not realistic to obtain the number by simple backtracking. As a recent result, Ripatti reported the number of semi-magic squares of order 6 (the magic squares of 6 × 6 without diagonal sum conditions) in 2018. In this research, with reference to Ripatti's method of enumerating semi-magic squares, we have calculated the total number of associative magic squares of order 7. There are exactly 1,125,154,039,419,854,784 associative magic squares of order 7 excluding symmetric patterns. ------------------------------ This is a preprint of an article intended for publication Journal of Information Processing(JIP). This preprint should not be cited. This article should be cited as: Journal of Information Processing Vol.28(2020) (online) DOI http://dx.doi.org/10.2197/ipsjjip.28.903 ------------------------------ |
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| 書誌レコードID | ||||||||||
| 収録物識別子タイプ | NCID | |||||||||
| 収録物識別子 | AN00116647 | |||||||||
| 書誌情報 |
情報処理学会論文誌 巻 61, 号 12, 発行日 2020-12-15 |
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| ISSN | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 1882-7764 | |||||||||
