Teaching

Math 155R (Fall 2026)

Meets: Tuesdays and Thursdays during the Fall 2026 semester from 12 to 1:15 pm at Science Center 228.
Office hours: Thursday 1:30 to 2:30 pm and by appointment.

Course Assistants:

• Austin Luo (aluo@college.harvard.edu). OH: Wednesdays from 8 to 10 pm (Eliot Dining Hall).
• Stella Li (stellali@college.harvard.edu). OH: Mondays from 8 to 10 pm (Leverett Dining Hall).

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): Labeled structures and exponential generating functions
• Midterm 1 (Tue, Oct. 6)
• Lecture 10 (Thu, Oct. 8): Some probability
• Lecture 11 (Tue, Oct. 13): The Lindström–Gessel–Viennot lemma
• Lecture 12 (Thu, Oct. 15): Representation theory of finite groups
• Lecture 13 (Tue, Oct. 20): Examples of representations
• Lecture 14 (Thu, Oct. 22): Schur’s lemma and Maschke’s theorem
• Lecture 15 (Tue, Oct. 27): Conjugacy classes and orthogonality of characters
• Lecture 16 (Thu, Oct. 29): Character tables
• Lecture 17 (Tue, Nov. 3): Specht modules
• Lecture 18 (Thu, Nov. 5): The Robinson–Schensted algorithm
• Midterm 2 (Tue, Nov. 10)
• Lecture 19 (Thu, Nov. 12): Shadow diagrams and jeu de taquin
• Lecture 20 (Tue, Nov. 17): The hook-length formula
• Lecture 21 (Thu, Nov. 19): TBA
• Lecture 22 (Tue, Nov. 24): TBA
• No class (Thu, Nov. 26): Thanksgiving recess
• Lecture 23 (Tue, Dec. 1): Final project presentations
• Lecture 24 (Thu, Dec. 3): Final project presentations