Math 68
Algebraic Combinatorics
Last updated June 27, 2016 13:25:50 EDT
Tentative syllabus
Here is a tentative list of topics that will be convered, together with the corresponding references.
- Basic combinatorics.
- Catalan numbers. Sets and multisets. Compositions.
[dM] Chapter 1.
Other references: [Aig] Sections 1.1-1.2. [EC1] Section 1.2.
- Integer and set partitions. Stirling numbers. Permutations.
[dM] Chapter 3.
Other references: [Aig] Sections 1.3-1.5. [vLW] Chapter 13. [EC1] Section 1.3.
- Inclusion-Exclusion.
[dM] Chapter 2.
Other references: [Aig] Section 5.1. [EC1] Sections 2.1-2.3. [vLW] Chapter 10.
- Generating functions.
- Recurrences. Formal power series.
[dM] Chapter 4.
Other references: [Aig] Sections 2.1, 2.2, 3.1. [Wf] Section 2.1. [vLW] Chapter 14.
- The symbolic method. Unlabeled structures. Ordinary generating functions.
[dM] Chapter 5.
Other references: [FS] Chapter 1. [Wf] Section 2.2.
- Labeled structures. Exponential generating functions.
[dM] Chapter 6.
Other references: [Aig] Section 3.3. [FS] Chapter 2. [Wf] Section 2.3.
- Topics in algebraic combinatorics.
- Partially ordered sets. Chains and antichains. Sperner's theorem.
[St] Chapter 4.
- Young tableaux. The RSK algorithm.
[St] Chapter 8.
Other references: [EC2] Section 7.11. [BS] Section 4.
- Group actions on boolean algebras.
[St] Chapter 5.
- Young diagrams and q-binomial coefficients.
[St] Chapter 6.
Other references: [Aig] Section 1.6.
- Enumeration under group action. Counting orbits using the Burnside Lemma. Polya's theorem.
[St] Chapter 7.
Other references: [Aig] Sections 6.1-6.3.
Last updated June 27, 2016 13:25:50 EDT