組合學導論
Introduction to Combinatorics
| 節 | 週一 | 週三 |
|---|---|---|
3 10:10–11:00 | 組合學導論 SA223（光復） 2 節連堂 | |
4 11:10–12:00 | 組合學導論 SA223（光復） |
* 根據陽明交大上課時間表所列
This is a required course of the Combinatorics Graduate Program. The syllabus of the course will contain half of the topics from the Ph.D. qualification exam of combinatorics (the other half will be taught in the course "Graph Theory").
Undergraduate Discrete Mathematics and Linear Algebra.
無備註
相關事項將公佈於e3(https://e3p.nycu.edu.tw/)。 助教名單與其值班時間將公佈於e3。
1.出席 10%, 2.作業 30%, 4.期中考 30%, 5.期末考 30%。
6. Dilworth's theorem and extremal set theory
Partially ordered sets, Dilworth's theorem, Sperner's theorem, symmetric chains, the Erdős-Ko-Rado theorem
- 講授：
- 2
10. The principle of inclusion and exclusion; inversion formulae
Inclusion–exclusion, derangements, Euler indicator, Möbius function, Möbius inversion, Burnside's lemma, problème des ménages
- 講授：
- 2
13. Elementary counting; Stirling numbers
Stirling numbers of the first and second kind, Bell numbers, generating functions
- 講授：
- 2.5
14. Recursions and generating functions
Elementary recurrences, Catalan numbers, counting of trees, Joyal theory, Lagrange inversion
- 講授：
- 6
15. Partitions
The function p_k(n) , the partition function, Ferrers diagrams, Euler's identity, asymptotics, the Jacobi triple product identity, Young tableaux and the hook formula
- 講授：
- 4
17. Latin squares
Orthogonal arrays, conjugates and isomorphism, partial and incomplete Latin squares, counting Latin squares, the Evans conjecture, the Dinitz conjecture
- 講授：
- 4.5
22. Orthogonal Latin squares
Pairwise orthogonal Latin squares and nets, Euler's conjecture, the Bose-Parker-Shrikhande theorem, asymptotic existence, orthogonal arrays and transversal designs, difference methods, orthogonal subsquares
- 講授：
- 5
19. Designs
The Erdős-De Bruijn theorem, Steiner systems, balanced incomplete block designs, Hadamard designs, counting, (higher) incidence matrices, the Wilson-Petrenjuk theorem, symmetric designs, projective planes, derived and residual designs, the Bruck-Ryser-Chowla theorem, constructions of Steiner triple systems, write-once memories
- 講授：
- 7
25. Lattices and Möbius inversion
The incidence algebra of a poset, the Möbius function, chromatic polynomial of a graph, Weisner's theorem, complementing permutations of geometric lattices, connected labeled graphs, MDS codes
- 講授：
- 4.5
37. Pólya theory of counting
The cycle index of a permutation group, counting orbits, weights, necklaces, the symmetric group, Stirling numbers
- 講授：
- 3.5
| 週次 | 主題 |
|---|---|
| 第 1 週 | 2024-02-19(一),2024-02-21(三) |
| 第 2 週 | 2024-02-26(一),2024-02-28(三) |
| 第 3 週 | 2024-03-04(一),2024-03-06(三) |
| 第 4 週 | 2024-03-11(一),2024-03-13(三) |
| 第 5 週 | 2024-03-18(一),2024-03-20(三) |
| 第 6 週 | 2024-03-25(一),2024-03-27(三) |
| 第 7 週 | 2024-04-01(一),2024-04-03(三) |
| 第 8 週 | 2024-04-08(一),2024-04-10(三) |
| 第 9 週 | 2024-04-15(一),2024-04-17(三) |
| 第 10 週 | 2024-04-22(一),2024-04-24(三) |
| 第 11 週 | 2024-04-29(一),2024-05-01(三) |
| 第 12 週 | 2024-05-06(一),2024-05-08(三) |
| 第 13 週 | 2024-05-13(一),2024-05-15(三) |
| 第 14 週 | 2024-05-20(一),2024-05-22(三) |
| 第 15 週 | 2024-05-27(一),2024-05-29(三) |
| 第 16 週 | 2024-06-03(一),2024-06-05(三) |
| 第 17 週 | 2024-06-10(一),2024-06-12(三) |
| 第 18 週 | 2024-06-17(一),2024-06-19(三) |
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, 2nd Ed., Cambridge University Press.
- 地點
- 科一館SA231
- 時間
- 約定時間
- 聯絡方式
- E-mail:wuhsiunglin@nctu.edu.tw 校內分機: 03-5712121#56438