In algebraic combinatorics one associates algebraic objects like groups, rings and vector spaces to combinatorial objects in order to reveal more of their structure, therefore we introduce students in this class basic knowledge regarding algebraic tools and related combinatorial objects, and also directions for further research. More precisely, the following will be covered:
(1) elementary number theory, groups, rings, fields, and vector spaces;
(2) graphs, recurrences, generating functions, and enumeration principles;
(3) advanced combinatorics such as Mobius inversion formula, Polya theory of counting etc.;
(4) topics in algebraic graph theory;
(5) topics in algebraic combinatorics.In algebraic combinatorics one associates algebraic objects like groups, rings and vector spaces to combiner objects in order to reveal more of their structure, therefore we introduce students in this class basic knowledge regarding algebraic tools and related combinatorial objects, and also directions for further research. More precisely, the following will be covered:
(1) elementary number theory, groups, rings, fields, and vector spaces;
(2) graphs, recurrences, generating functions, and enumeration principles;
(3) advanced combinatorics such as Mobius inversion formula, Polya theory of counting etc.;
(4) topics in algebraic graph theory;
(5) topics in algebraic combiner.
- Richard Stanley, Enumerative Combinatorics, Volume 1, Cambridge University Press
- Richard Stanley, Topics in Algebraic Combinatorics, MIT.
- Lecture Notes of the Instructor.
- Richard Stanley, Enumerative Combinatorics, Volume 1, Cambridge University Press
- Richard Stanley, Topics in Algebraic Combinatorics, MIT.
- Lecture Notes of the Instructor.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| midterm exammidterm exam midterm exam |
40 | |
| oral presentationoral presentation oral presentation |
30 | 口頭報告 |
| written reportwritten report written report |
30 | 書面報告 |
