• Partitions [EC 1.8, BS 2, AE, An, Br, Notes]
  
  • Generating functions for partitions
  • Euler's pentagonal number theorem
  • Jacobi's triple product identity
  • Rogers-Ramanujan identities [For applications to physics, see this article.]
  • Bijective proofs of classical partition identities, partitions avoiding multisets of parts
  • The involution principle [EC 2.6]
  • Examples of the involution principle
  • Lecture hall partitions
  
  
• Tableaux, plane partitions, tilings, and lattice paths [Br, BS 3-9, EC, Notes]
  
  • Plane partitions, MacMahon's theorem [BS 3]
  • Refinements of MacMahon's theorem
  • Symmetric, cyclically symmetric, and totally symmetric plane partitions [Br]
  • P-partitions [EC 3.15]
  • Reverse plane partitions, the Hillman-Grassl bijection, the hook-length formula
  • Reduced decompositions, the Edelman-Greene bijection [BS 7]
  • Domino tilings of rectangles and Aztec diamonds [BS 8], connections of tilings to plane partitions [BS 9]
  • Determinants, the Gessel-Viennot formula [EC 2.7]
  • Labeled trees, parking functions
  • Inclusion-exclusion [EC 2.1]
  
  

• Friday, May 10: Kassie and Tim, A combinatorial proof of the Rogers-Ramanujan identities.
• Monday, May 13: Zach, Generalized vexillary permutations and Stanley symmetric functions.
• Monday, May 20: Jenny, The enumeration of lecture hall partitions.
• Wednesday, May 22: Megan, The alternating sign matrix conjecture. Jonathan, Determinants, nonintersecting paths, and Young tableaux.
• Friday, May 24: Seth, A combinatorial proof of the unimodality of the q-binomial coefficients.
• Wednesday, May 29: Eva, A bijection between k-triangulations and k-tuples of non-intersecting Dyck paths. David, Permutohedra and associahedra.

Last updated June 27, 2016 13:25:41 EDT