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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
https://ompu.repo.nii.ac.jp/records/517
https://ompu.repo.nii.ac.jp/records/5173485a82b-a03e-46c6-94dc-5e0680f1365e
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
1-2_論文_永田誠・武井由智 (1.3 MB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2023-05-01 | |||||
| タイトル | ||||||
| タイトル | 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 | |||||
| タイトル | ||||||
| タイトル | On a 2-dimensional version of Sur´anyi’s bijections for S´os permutations | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | jpn | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Farey diagram | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Farey sequence | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | S´os permutation | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Sur´anyi’s bijection | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | symmetric group | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Young tableau | |||||
| 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 | departmental bulletin paper | |||||
| 著者 |
永田, 誠
× 永田, 誠× 武井, 由智× NAGATA, Makoto× TAKEI, Yoshinori |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We consider a 2-dimensional version of Sur´anyi’s bijections for S´os permutations. Sur´anyi’s bijection is a bijective map between the set of the short intervals appearing as the division of the unit interval by the Farey sequence and the set of S´os permutations. A concept equivalent to Sur´anyi’s bijection is a bijective map between the set of the short intervals by the Farey sequence and the set of the inverses of S´os permutations. In this article, we attempt to give a 2-dimensional analogue of the latter map. First, we introduce our 2D version, which we refer to as a ranking table, of the inverse of a S´os permutation. Then we define small polygons, which are bounded by the lines of so-called Farey diagram and some additional lines, as our 2D version of the short intervals by the Farey sequence. Based on these definitions, we show that our map between the set of the small polygons and the set of the ranking tables is a well-defined surjection. Also, an examination using a computer shows that the map is in fact bijective, for all 81 cases (which can be reduced to 45 cases by a symmetry) which are chosen as the cases in which the size of the ranking table is small. Furthermore, we show that our map is indeed injective when the image of the map is restricted to the set of the ranking tables formed by the standard Young tableaux. This restricted map may be interpreted as yet another Sur´anyi’s bijection which is different from our 2D version. In fact, the domain which is similar to the short intervals by Farey sequences appears for our bijective map into the set of Young tableaux. We also mention the triangles-quadrangles conjecture for the Farey diagram in our context. |
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| 書誌情報 |
大阪医科薬科大学 薬学部雑誌 en : Bulletin of the Faculty of Pharmacy, Osaka Medical and Pharmaceutical University 巻 2, p. 21-55, 発行日 2023-03-28 |
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| 出版者 | ||||||
| 出版者 | 大阪医科薬科大学薬学部 | |||||
