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