Teaching

Math 155R

Meets: Tuesdays and Thursdays during the Fall 2026 semester from 12pm to 1:15pm at Science Center 228.
Office hours: Thursday 1:30-12:00 and by appointment

Course

Math 155R will be an introduction to enumerative and algebraic combinatorics. The course will introduce several classes of combinatorial objects (permutations, Dyck paths, trees…) as well as some classical methods used to enumerate them. The course will then cover topics related to the combinatorics of the representation theory of the symmetric group such as Young tableaux, the hook-length formula and the Robinson-Schensted correspondence.

References

The main references will be:

• Stanley: Enumerative Combinatorics I & II
• Bruce Sagan: The Symmetric Group
• Philippe Flajolet, Robert Sedgewick: Analytic Combinatorics.

Prerequisites: Basic linear algebra and also basic abstract algebra (such as from Math 122).

Tentative schedule

• Lecture 1 (Thu, Sept. 3): Outline of the course
• Lecture 2 (Tue, Sept. 8): Combinatorial classes and generating functions
• Lecture 3 (Thu, Sept. 10): Some classical combinatorial objects
• Lecture 4 (Tue, Sept. 15): Tree structures
• Lecture 5 (Thu, Sept. 17): Lagrange inversion formula
• Lecture 6 (Tue, Sept. 22): Cartier–Foata monoids
• Lecture 7 (Thu, Sept. 24): The transfer-matrix method
• Lecture 8 (Tue, Sept. 29): Viennot’s theorem
• Lecture 9 (Thu, Oct. 1): Labelled structures and exponential generating functions
• Midterm 1 (Tue, Oct. 6)
• Lecture 10 (Thu, Oct. 8): Cayley’s formula
• Lecture 11 (Tue, Oct. 13): The Lindström–Gessel–Viennot lemma
• Lecture 12 (Thu, Oct. 15): Planar maps and Tutte recursion
• Lecture 13 (Tue, Oct. 20): Representation theory of finite groups
• Lecture 14 (Thu, Oct. 22): Examples of representations
• Lecture 15 (Tue, Oct. 27): Schur’s lemma and Maschke’s theorem
• Lecture 16 (Thu, Oct. 29): Conjugacy classes and orthogonality of characters
• Lecture 17 (Tue, Nov. 3): Character tables
• Lecture 18 (Thu, Nov. 5): Specht modules
• Midterm 2 (Tue, Nov. 10)
• Lecture 19 (Thu, Nov. 12): The Robinson–Schensted algorithm
• Lecture 20 (Tue, Nov. 17): Shadow diagrams and jeu de taquin
• Lecture 21 (Thu, Nov. 19): The hook-length formula
• Lecture 22 (Tue, Nov. 24):
• No class (Thu, Nov. 26): Thanksgiving recess
• Lecture 23 (Tue, Dec. 1): Final project presentations
• Lecture 24 (Thu, Dec. 3): Final project presentations