## 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 November 01, 2016 09:23:32 EDT