Math 68, Fall 2019

Algebraic Combinatorics
Last updated September 10, 2019 16:27:27 EDT

Course Objectives: Algebraic combinatorics is defined as the interactions between algebra and combinatorics. Techniques from algebra may solve combinatorial problem and conversely. The goal of this class is to introduce some notions of combinatorics and to use the techniques from it along with linear and abstract algebra. The first part of the course will be dedicated to review principles from enumerative combinatorics, such as basic statistics, counting principles and generating functions. Going forward, we will apply these to three main topics:

  • Partial ordered sets (posets), lattices, Möbius function and incidence algebra. Sperner’s lemma.

  • Group acting on a set and Pólya theory.
  • Representation theory of the symmetric group and Young tableaux. Robinson- Schensted bijection and applications to permutation patterns. Promotion and evacuation, branching rule.

Teaching Methods & Philosophy

Throughout the semester, the blackboard will be the main tool for in-class teaching. That being said, I would like to make some computer demonstrations and I plan to include some time for the students to work on short problems together. Some non- graded and anonymous quizzes will be held during the class, and this is for me and you to know what you understood well and what should be covered more deeply.