Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

Graduate Combinatorics is not a formal class at ETSU. These notes are meant for self-study and reference. An errata for the book is available online.

• Preface.
• Chapter 1. Basic Counting.
• Chapter 2. Counting with Signs.
• Chapter 3. Counting with Ordinary Generating Functions.
• Chapter 4. Counting with Expontential Generating Functions.
• Chapter 5. Counting with Partially Ordered Sets.
• Chapter 6. Counting with Group Actions.
• Chapter 7. Counting with Symmetric Functions.
• Chapter 8. Counting with Quasisymmetric Functions.
• Appendix.

Preface. Preface notes

Chapter 1. Basic Counting.

• Section 1.1. The Sum and Product Rules for Sets. Section 1.1 notes
• Supplement. Proofs of Theorems in Section 1.1. Beamer file of Section 1.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 1.1. Print file of Section 1.1 proofs
• Section 1.2. Permutations and Words. Section 1.2 notes
• Supplement. Proofs of Theorems in Section 1.2. Beamer file of Section 1.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section 1.2. Print file of Section 1.2 proofs
• Section 1.3. Combinations and Subsets. Section 1.3 notes
• Section 1.4. Set Partititions.
• Section 1.5. Permutations by Cycle and Structure.
• Section 1.6. Integer Partitions.
• Section 1.7. Compositions.
• Section 1.8. The Twelvefold Way.
• Section 1.9. Graphs and Digraphs.
• Section 1.10. Trees.
• Section 1.11. Lattice Paths.
• Section 1.12. Pattern Avoidance.
• Study Guide 1.

Chapter 2. Counting with Signs.

• Section 2.1. The Principle of Inclusion and Exclusion.
• Section 2.2. Sign-Reversing Involutions.
• Section 2.3. The Garsia-Milne Involution Principle.
• Section 2.4. The Reflection Principle.
• Section 2.5. The Lindström-Gessel-Viennot Lemma.
• Section 2.6. The Matrix-Tree Theorem.
• Study Guide 2.

Chapter 3. Counting with Ordinary Generating Functions.

• Section 3.1. Generating Polynomials.
• Section 3.2. Statistics and q-Analogues.
• Section 3.3. The Algebra of Formal Power Series.
• Section 3.4. The Sum and Product Rulrs for ogfs.
• Section 3.5. Revisiting Integer Partitions.
• Section 3.6. Recurrence Relations and Generating Functions.
• Section 3.7. Rational Generating Functions and Linear Recursions.
• Section 3.8. Chromatic Polynomials.
• Section 3.9. Combinatorial Reciprocity.
• Study Guide 3.

Chapter 4. Counting with Expontential Generating Functions.

• Section 4.1. First Examples.
• Section 4.2. Generating Functions for Eulerian Polynomials.
• Section 4.3. Labeled Structures.
• Section 4.4. The Sum and Product Rules for egfs.
• Section 4.5. The Exponential Formula.
• Study Guide 4.

Chapter 5. Counting with Partially Ordered Sets.

• Section 5.1. Basic Properties of Partially Ordered Sets.
• Section 5.2. Chains, Antichains, and Operations on Posets.
• Section 5.3. Lattices.
• Section 5.4. The Möbius Function of a Poset.
• Section 5.5. The Möbius Inversion Theorem.
• Section 5.6. Characteristic Polynomials.
• Section 5.7. Quotients of Posets.
• Section 5.8. Computing the Möbius Function.
• Section 5.9. Binomial Posets.
• Study Guide 5.

Chapter 6. Counting with Group Actions.

• Section 6.1. Groups Acting on Sets.
• Section 6.2. Burnside's Lemma.
• Section 6.3. The Cycle Index.
• Section 6.4. Redfield-Pólya Theory.
• Section 6.5. An Application to Proving Congruences.
• Section 6.6. The Cyclic Sieving Phenomenon.
• Study Guide 6.

Chapter 7. Counting with Symmetric Functions.

• Section 7.1. The Algebra of Symmtric Functions, Sym.
• Section 7.2. The Schur Basis of Sym.
• Section 7.3. Hooklengths.
• Section 7.4. P-Partitions.
• Section 7.5. The Robinson-Schensted-Kntuh Correspondence.
• Section 7.6. Longest Increasing and Decreasing Subsequences.
• Section 7.7. Differential Posets.
• Section 7.8. The Chromatic Symmetric Function.
• Section 7.9. Cyclic Sieving Redux.
• Study Guide 7.

Chapter 8. Counting with Quasisymmetric Functions.

• Section 8.1. The Algebra of Quasisymmetric Functions, QSym.
• Section 8.2. Reverse P-Partitions.
• Section 8.3. Chain Enumeration in Posets.
• Section 8.4. Pattern Avoidance and Quasisymmetric Functions.
• Section 8.5. The Chromatic Quasisymmetric Function.
• Study Guide 8.

Appendix.

• Appendix A1. Basic Notions.

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