Tentative syllabus
The following is a list of topics that I'd like to cover, together with references (click here for book information). This page will be updated as the course progresses.
- Permutations [EC Ch 1, Bo Ch 1-3, St]
- How to count [EC 1.1, see also What is an answer? and Enumerative and algebraic combinatorics]
- Cycles, left-to-right maxima, inversions [EC 1.3]
- Descents, Eulerian numbers, major index, excedances [EC 1.4]
- Geometric representations of permutations, increasing trees [EC 1.5]
- Alternating permutations, Euler numbers [EC 1.6, St]
- Permutations of multisets, q-binomial coefficients [EC 1.7]
- Partitions and tableaux [EC, BS 2-9, AE, An, Br, St, Notes]
- Generating functions for partitions [EC 1.8, BS2]
- Euler's pentagonal number theorem [EC 1.8]
- Jacobi's triple product identity
- Rogers-Ramanujan identities [For applications to physics, see this article]
- Lecture hall partitions
- Standard Young tableaux, the Hook-length formula [BS 4]
- The RSK algorithm [EC 7.11, 7.13, Bo 7.1]
- Increasing and decreasing subsequences [BS 6, St]
- Plane partitions, MacMahon's theorem [BS 3]
- Reduced decompositions, the Edelman-Greene bijection [BS 7, St]
- Domino tilings of rectangles and Aztec diamonds [BS 8], connections of tilings to plane partitions [BS 9]
- Lattice paths [EC Ch 2, Notes]
- Dyck paths, Motzkin paths
- Bijections for lattice paths
- Paths between two boundaries
- Determinants, the Gessel-Viennot formula [EC 2.7]
Last updated August 11, 2020 16:04:36 EDT