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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70932完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 葉永南(Yeong-Nan Yeh) | |
| dc.contributor.author | Shiuan Fu | en |
| dc.contributor.author | 傅璿 | zh_TW |
| dc.date.accessioned | 2021-06-17T04:44:31Z | - |
| dc.date.available | 2018-11-02 | |
| dc.date.copyright | 2018-08-07 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-08-02 | |
| dc.identifier.citation | [1] M. D. Atkinson, Restricted permutations, Discrete Mathematics 195 (1999) 27-38
[2] M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. Handley and D. Holton, Permutations of a Multiset Avoiding Permutations of Length 3, Europ. J. Combinatorics (2001) 22, 1021–1031 [3] C. Banderier, P. Flajolet, D. Gardy, M. Bousquet-Melou, A. Denise, D. GouyouBeauchamps, Generating functions for generating trees, Discrete Mathematics 246 (1-3) (2002) 29-55 [4] F. R. K. Chung, R. L. Graham, V. E. Hoggatt, Jr., M. Kleiman, The number of Baxter permutations, Journal of Combinatorial Theory, Series A, 24, 382–394 (1978) [5] D. Callan, S. M. Ma, T. Mansour, Restricted Stirling Permutations, Taiwanese Journal of Mathematics (2016) Vol. 20, No. 5, 957–978 [6] S. Dulucq, S. Gire, J. West, Permutations with forbidden subsequences and nonseparable planar maps, Discrete Mathematics 153 (1996) 85-103 [7] S. Dulucq, S. Gire, O. Guibert, A combinatorial proof of J.West′s conjecture, Discrete Mathematics 187 (1998) 71-96 [8] G. H. Duh, Y. C. R. Lin, S. M. Ma, Y. N. Yeh, Some statistics on Stirling permutations and Stirling derangements, Discrete Mathematics 341 (2018) 2478–2484 [9] I. Gessel, R. P. Stanley, Stirling polynomials, Journal of Combinatorial Theory, Series A 24, 24-33 (1978) [10] O. Guibert, Stack words, standard Young tableaux, permutations with forbidden subsequences and planar maps, Discrete Mathematics 210 (2000) 71–85 [11] D. E. Knuth,The art of computer programming, vol.1, 1st Edition, Addison-Wesley (1968) [12] M. Kuba, A. Panholzer, Enumeration formulæ for pattern restricted Stirling permutations, Discrete Mathematics 312 (2012) 3179–3194 [13] R. Simon, F. W. Schmidt, Restricted Permutations, Europ.J. Combinatorics (1985) 6, 383-406 [14] W. T. Tutte, A census of planar maps, Canadian Journal of Mathematics (1963) [15] J. West, Permutations with forbidden subsequences and stack-sortable permutations, Ph.D. Thesis, MIT, Cambridge, MA, 1990 [16] D. Zeilberger, A proof of Julian West′s conjecture that the number of two-stack sortable permutations of length n is 2(3n)!/((n+1)!(2n+1)!), Discrete Mathematics. 102 (1992) 85–93 [17]“Baxter permutation.”, Wikipedia, Wikimedia Foundation, 19 June 2018, en.wikipedia.org/wiki/Baxter_permutation [18]“Permutation Pattern.”, Wikipedia, Wikimedia Foundation, 27 June 2018, en.wikipedia.org/wiki/Permutation_pattern | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70932 | - |
| dc.description.abstract | The goal of this thesis is to derive properties for the generating functions of σ-pattern avoiding Stirling derangements where σ is a permutation in the symmetric group S3.
This thesis is organized as follows: In chapter 1, we roughly make a introduction to the history of pattern avoiding sequences. In chapter 2, we state the kernel method. In chapter 3, we derive the generating functions of σ-pattern avoiding Stirling derangements where σ is a permutation in S3. Since there are 6 cases, the main results will be stated by 6 main theorems. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T04:44:31Z (GMT). No. of bitstreams: 1 ntu-107-R05221013-1.pdf: 910581 bytes, checksum: eee291426da00fb31f0ed5ade580de52 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee (in Chinese) I
Acknowledgements (in Chinese) II Abstract (in Chinese) III Abstract (in English) IV 1 Introduction 1 2 Kernel method 13 3 Main Results 19 3.1 321-avoiding Stirling derangements 19 3.2 312-avoiding Stirling derangements 28 3.3 231-avoiding Stirling derangements 34 3.4 213-avoiding Stirling derangements 36 3.5 132-avoiding Stirling derangements 42 3.6 123-avoiding Stirling derangements 47 3.7 Summary table 51 Reference 53 | |
| dc.language.iso | en | |
| dc.subject | Stirling排列 | zh_TW |
| dc.subject | 錯位排列 | zh_TW |
| dc.subject | 字串禁位 | zh_TW |
| dc.subject | 生成函數 | zh_TW |
| dc.subject | 核方法 | zh_TW |
| dc.subject | Pattern avoidance | en |
| dc.subject | Generating function | en |
| dc.subject | Stirling permutation | en |
| dc.subject | Derangement | en |
| dc.subject | Kernel method | en |
| dc.title | 字串禁位Stirling錯排的研究 | zh_TW |
| dc.title | On Pattern Avoiding Stirling Derangements | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 林惠雯(Hui-Wen Lin) | |
| dc.contributor.oralexamcommittee | 周文賢(Wun-Seng Chou),馬俊(Jun Ma),馬世美(Shi-Mei Ma) | |
| dc.subject.keyword | Stirling排列,錯位排列,字串禁位,生成函數,核方法, | zh_TW |
| dc.subject.keyword | Stirling permutation,Derangement,Pattern avoidance,Generating function,Kernel method, | en |
| dc.relation.page | 55 | |
| dc.identifier.doi | 10.6342/NTU201802156 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-08-03 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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