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Conjugate!

Math 502: Combinatorics II

This is the second semester of an introductory graduate-level course on combinatorics. We will be covering symmetric function theory, Young tableaux, counting with group actions, designs, matroids, finite geometries, and not-so-finite geometries.

Syllabus

For more details, see the Course Syllabus.

Resources

Recommended (but optional) books are listed in the Syllabus above.

Lecture notes will be updated here as the course progresses.

Jan 20, 23 - Intro and Antisymmetrics

Jan 25 - Omega involution

Jan 27 - Hall inner product

Jan 30, Feb 1, 3 - RSK and the Pieri rules

Feb 6, 8, 20 - RSK, Knuth equivalence, and JDT

Feb 13, 15, 17 - Littlewood-Richardson tableaux and crystals

Feb 20, 22, 24, 27 - Crash course on representation theory

March 1, 3 - Characters and the Murnaghan-Nakayama rule

March 6, 8, 10 - Counting with group actions

March 20, 22, 24 - Designs

March [27] 29, 31 - Matroids

Apr 3, 5, 7 - Matroids II

Apr 10, 12, 14 - Finite Geometries

Apr 17, 19, 21 - Not So Finite Geometries

Office hours

My office is Weber 125, near the west door of the tea room. Come find me:

Homework

Homework assignments will be posted here as the course progresses.

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Homework 9

Homework 10

Homework 11

Homework 12

Homework 13

Homework 14

Final Projects

Here are the final projects written by the students:

C. Mrozek and A. Romero, Hook Length Formula - History and Proofs by Example

P. Wilson, Promotion and Evacuation

C. Jones, What’s Your Strategy?

K. Brown, Local Evacuation Shuffling and the Pieri Case

I. Rojas, Moduli Spaces of Stable Curves with Marked Points: Examples and Connections to Trees

J. McCann, Solving Linear Intersection Problems with Schubert Varieties

T. Osland on Knutson-Tao Puzzles

I. Jorquera, Linear Independence of Frames