研究生: |
周孟謙 Chou, Meng-Chien |
---|---|
論文名稱: |
On Schur expansions of Petrie Symmetric functions multiplied by a power symmetric function On Schur expansions of Petrie Symmetric functions multiplied by a power symmetric function |
指導教授: |
游森棚
Eu, Sen-Peng |
口試委員: |
游森棚
Eu, Sen-Peng 郭君逸 Guo, Jun-Yi 丁建太 Ting, Chien-Tai |
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: | 27 |
英文關鍵詞: | symmetric functions, Schur functions, Petrie symmetric function |
DOI URL: | http://doi.org/10.6345/NTNU202200720 |
論文種類: | 學術論文 |
相關次數: | 點閱:90 下載:23 |
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在 [2] 中,Darij Grinberg 證明了 Petrie symmetric function 是 signed multiplicity-free ,並使用代數的方法證明 Liu–Polo conjecture。本文章的主要結果是我們找到了組合的方法計算 k-Petrie number,因此我們可以知道 Petrie symmetric function 可以寫成那些 Schur functions 的線性組合。由這個組合解釋,Liu–Polo conjecture 有了簡單的證明;我們也用這個組合解釋證明並推廣了 Alexandersson conjecture。
[1] Gordon James and Adalbert Kerber. The representation theory of the symmetric group. Cambridge University Press, 1984.
[2] Darij Grinberg, Petrie symmetric functions, arXiv:2004.11194.
[3] R. P. Stanley, Enumerative Combinatorics (Volume 2), second edition (2011)
[4] Stephen Doty, Grant Walker, Modular symmetric functions and irreducible modular representations of general linear groups, J. Pure Appl. Algebra 82 (1992), no. 1, pp. 1–26.
[5] Grant Walker, Modular Schur functions, Trans. Amer. Math. Soc. 346 (1994), pp. 569–604.
[6] Houshan Fu, Zhousheng Mei, Truncated Homogeneous Symmetric Functions, Linear and Multilinear Algebra, 70:3, 438-448, DOI: 10.1080/03081087.2020.1733460
[7] Manfred Gordon, E. Martin Wilkinson, Determinants of Petrie matrices, Pacific Journal of Mathematics 51, no. 2, 1974.
[8] Bergeron, François. Algebraic combinatorics and coinvariant spaces. CRC Press, 2009.