Here is a tentative list of topics that will be covered, together with the corresponding references.

 Main reference Other references Basic combinatorics Catalan numbers. Sets and multisets. Compositions. [dM] Chapter 1 [Aig] Sections 1.1-1.2[EC1] Section 1.2 Integer and set partitions. Stirling numbers. Permutations. [dM] Chapter 3 [Aig] Sections 1.3-1.5[vLW] Chapter 13[EC1] Section 1.3. Inclusion-Exclusion. [dM] Chapter 2 [Aig] Section 5.1[EC1] Sections 2.1-2.3[vLW] Chapter 10 Generating functions Recurrences. Formal power series. [dM] Chapter 4 [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 [FS] Chapter 1[Wf] Section 2.2 Labeled structures. Exponential generating functions. [dM] Chapter 6 [Aig] Section 3.3[FS] Chapter 2[Wf] Section 2.3 Topics in algebraic combinatorics Enumeration under group action.Counting orbits using the Burnside Lemma. Polya's theorem. [St] Chapter 7 [Aig] Sections 6.1-6.3 Partially ordered sets. Chains and antichains.Sperner's theorem. [St] Chapter 4 Young tableaux. The hook-length formula. Operators on Young's lattice. [St] Chapter 8 [EC2] Section 7.11[BS] Section 4

This is a more accurate description of the topics covered each day so far:

 Day 1: Lattice paths, Dyck paths, the reflection principle, rotated paths, recurrences Day 2: Binomial coefficients, multisets, compositions, partitions Day 3: More partitions, set partitions, Stirling numbers, cycles in permutations Day 4: Permutation statistics: cycles, records, descents, inversions Day 5: Inversion table, major index, fixed points, derangements; inclusion-exclusion Day 6: More inclusion-exclusion, answers to enumeration questions, generating functions Day 7: The ring of formal power series, operations with generating functions Day 8: Linear recurrences and rational generating functions; a non-linear recurrence Day 9: The symbolic method for unlabeled structures, operations on combinatorial classes Day 10: Ordinary generating functions for words, compositions, partitions, plane trees Day 11: Binary trees, set partitions; the symbolic method for labeled structures Day 12: The labeled product, sequences and sets of labeled classes; labeled rooted trees, set partitions Day 13: Cycles of labeled classes; surjective maps, labeled graphs, permutations, involutions; multivariate generating functions Day 14: The Lagrange inversion formula, Cayley's formula and Prufer code Day 15: Group actions, orbits, equivalent colorings Day 16: [Justin] Enumeration under group action Day 17: [Justin] Enumeration under group action Day 18: [Justin] Enumeration under group action Day 19: Applications of Polya's theorem: necklaces, dihedral necklaces, Stirling numbers Day 20: Partially ordered sets, graded posets, chains, antichains Day 21: Sperner's theorem, order matchings using linear algebra Day 22: Finishing the algebraic proof of Sperner's theorem; Lubell's proof Day 23 -Nov 1: Juan's presentation: A general partition theorem.Young's lattice, standard young tableaux Day 24 -Nov 3: Avery and Sophie's presentation: Walks in graphs.The hook-length formula Day 25 -Nov 6: Lizzie's presentation: The inversion number and the major index.Linear operators and walks in Young's lattice Day 26 -Nov 8: Sara and Emma's presentation: Two proofs of the hook-length formula Day 27 -Nov 10: Doug and Zach's presentation: Random walks in Zd Day 28 -Nov 13: Amir's presentation: A combinatorial proof of the Lagrange inversion formula Shikhin's presentation: The RSK correspondence