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| 研究生： |
陳俊友 Chen, Chun-Yu |
|---|---|
| 論文名稱： |
可推倒排列的刻劃與性質 The characterization and properties of toppleable permutations |
| 指導教授： |
游森棚
Eu, Sen-Peng |
| 口試委員： |
郭君逸
Guo, Jun-Yi 丁建太 Ting, Chien-Tai 游森棚 Eu, Sen-Peng |
| 口試日期： | 2022/06/08 |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2022 |
| 畢業學年度： | 110 |
| 語文別： | 中文 |
| 論文頁數： | 30 |
| 中文關鍵詞： | 可推倒排列 |
| 英文關鍵詞： | toppleable permutation, poly-Bernoulli number type B and C |
| 研究方法: | 比較研究 、 觀察研究 、 文件分析法 |
| DOI URL： | http://doi.org/10.6345/NTNU202200675 |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：51 下載：17 |
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本論文在第一章首先會先簡單介紹 toppleable permutation，然後在第二章針對 Arvind Ayyer, Daniel Hathcock 與 Prasad Tetali 等人 [1] 所提出的 rtoppleable permutation 做更進一步的刻劃，另外提出一些與 Arvind Ayyer and Beáta Bényi [2] 所提出的論文之相同與相異之處，最後在第三章提出一個關於數列 t(n, r) 的新結果，還有關於 poly-Bernoulli number type B 和 type C 做 gamma positive 的一些研究與正在整理的猜想。
In this paper, first we will introduce the toppleable permutation in Chapter 1, then we further describe the r-toppleable permutation proposed by Arvind Ayyer, Daniel Hathcock and Prasad Tetali et al.[1], also present some similarities and differences
with the paper presented by Arvind Ayyer and Beáta Bényi [2] in Chapter 2, the third chapter presents a new result about the sequence t(n, r), as well as some researches and conjectures that are being sorted out about the poly-Bernoulli number type B and type C being gamma positive.
[1] Arvind Ayyer, Daniel Hathcock, and Prasad Tetali. Toppleable permutations, excedances and acyclic orientations, arXiv:2010.11236, 2020.
[2] Arvind Ayyer and Beáta Bényi, Toppling on permutations with an extra chip, arXiv:2104.13654, 2021.
[3] P. J. Cameron, C. A. Glass, and R. U. Schumacher. Acyclic orientations and poly-bernoulli numbers. arXiv preprint arXiv:1412.3685, 2014.
[4] SHIKATA, Miku. Lonesum matrices and poly-Bernoulli numbers. 2011.
[5] KHERA, Jessica; LUNDBERG, Erik; MELCZER, Stephen. Asymptotic enumeration of lonesum matrices. Advances in Applied Mathematics, 2021, 123: 102118.
[6] Stéphane Launois, Combinatorics of H-primes in quantum matrices, 2005.
[7] Béata Bényi and Péter Hajnal. Combinatorics of poly-Bernoulli numbers. Studia Sci. Math. Hungar., 52(4):537–558, 2015.
[8] Bényi, Beáta, and Péter Hajnal. ”Poly-Bernoulli numbers and Eulerian numbers.” arXiv preprint arXiv:1804.01868, 2018.
[9] Athanasiadis, Christos A. ”Gamma-positivity in combinatorics and geometry.” arXiv preprint arXiv:1711.05983, 2017.
[10] Katalin Vesztergombi. Permutations with restriction of middle strength. Studia Sci. Math. Hungar., 9:181–185 (1975), 1974.
