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ある型の置換の個数についてII
https://ompu.repo.nii.ac.jp/records/288
https://ompu.repo.nii.ac.jp/records/288de73bac9-bc28-48bd-ac5b-50e138c4b87b
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
ある型の置換の個数について II (1.8 MB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2022-05-31 | |||||
| タイトル | ||||||
| タイトル | ある型の置換の個数についてII | |||||
| 言語 | ja | |||||
| タイトル | ||||||
| タイトル | On the numbers of permutations of certain types II | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | jpn | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | arithmetic progression | |||||
| 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 | symmetric group | |||||
| 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 | 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 a different perspective and observed that people tend to generate certain types of permutations, then defined types NAP (nearly arithmetic progression) and pNAP (pseudo-nearly arithmetic progression) of permutations as mathematical abstractions of such tendency [Nagata and Takei, Bull. OUPS 2020]. Then, in [Nagata and Takei, Bull. OUPS 2021], the number of permutations of these types were bounded by asserting that the set of the inverse permutations of S´os type, which are defined as the translation of so-called S´os permutations [S´os, Ann. Univ. Sci. Budapest. E¨otv¨os, Sect. Math. 1958] by a constant, include the set of the permutations of NAP type and are included in the set of the permutations of pNAP type. Especially, the authors obtained a lower bound of the number of the permutations of pNAP type as the number of the permutations of S´os type whose explicit formula is obtained from the number of 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 the assertion by computer experiments that the set of the inverses of S´os type-permutations is indeed the same as the set of the permutations of pNAP type as long as the degree n of the permutations is not greater than 50. Thus, a remaining problem of major interest is bounding the number of pNAP permutations from above. In this paper, we address this problem. One of our results is that pNAP and the inverses of S´os permutations satisfy essentially identical recurrence relation. It gives immediately an upper bound (n − 1)n2 of the number of permutations of pNAP type. We note that the upper bound is of 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 is given and used to enlarge the upper limit of the degrees n for which the observed property “pNAP is inverse-S´os-type” is confirmed to 1300 from 50 in our previous paper. |
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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 1, p. 19-45, 発行日 2022-03-28 |
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| 出版者 | ||||||
| 出版者 | 大阪医科薬科大学薬学部 | |||||
