Topics in Combinatorics IV

Michaelmas 2023

The Epiphany 2024 webpage

Time and place:   Lectures: Mon, Th 16:00 CG218
Problems classes:   Fri 16:00 TLC123, Weeks 2,4,6,8
Instructor: Pavel Tumarkin
e-mail: pavel dot tumarkin at durham dot ac dot uk
Office: MCS3009; Phone: 334-3085
Office hours: Mon 14:15-15:30 and by appointment

Textbooks:

Parts of the content of the first term can also be found in the following books:

Preliminary course content (subject to change): Catalan numbers, partitions and Young diagrams, set partitions, statistics on permutations, posets and lattices, Robinson-Schensted correspondence, parking functions, chip firing games, finite games and ADE classification

Schedule:

  • Week 1: Catalan numbers: definitions, examples, generating function
  • Week 2: Catalan numbers: further examples; partitions and Young diagrams. Problems class
  • Week 3: The hook length formula
  • Week 4: Set partitions. Problems class
  • Week 5: Exponential formula; statistics on permutations
  • Week 6: Partially ordered sets. Problems class
  • Week 7: Posets and lattices
  • Week 8: Linear extensions of posets; Robinson-Schensted correspondence. Problems class
  • Week 9: Properties of RSK
  • Week 10: Symmetries of RSK; games on graphs

    Handouts: (lecture notes, intended to be more or less up to date)

    Problems classes:

    Homeworks: There will be weekly homework assignments. Selected exercises are to be handed in on weeks 3, 5, 7, and 9