# MATH 146 (Algebraic Combinatorics) - Spring 2014, UC Davis

## Course description

This course is an introduction to algebraic combinatorics. We will cover topics with relations to algebra (linear algebra and some group theory), probability theory (random walks and Tsetlin libraries), and representation theory (partitions and Young tableaux).

1. Random Walks
Walks on graphs, cubes and the Radon transform, random walks, Tsetlin library

2. Posets
Sperner property

3. Young diagrams
q-binomial coefficients, Rogers-Ramanujan identities, generating functions for partitions, Young tableaux, RSK algorithm

## Sage examples

Walks on graphs: pdf or sage worksheet
The n-cube: pdf or sage worksheet
The Tsetlin library
Young's lattice and RSK

## Notes

Rogers-Ramanujan identities pdf
Symmetric chain decomposition of cyclic quotients of Boolean algebras pdf

## Problem sets

Homework 1: due April 11 in class: pdf

Homework 2: due April 18 in class: pdf

Homework 3: due April 25 in class: pdf

Homework 4: due May 2 in class: pdf

Midterm: in class on May 9.
The midterm will cover Chapters 1-4 and Chapter 6 from the beginning up to and including Theorem 6.6 (pg 57-63 in the print version of the book). It will have 3 problems, one asking for definitions and statements of the main theorems we covered in class, one problem with True/False question that you need to justify, and one problem on walks on graphs. Make sure you know how to compute the determinant of a 2x2 matrix and how to solve quadratic equations!

No homework due on May 9 due to midterm on May 9!!

Homework 5: due May 16 in class: pdf

Homework 6: due May 23 in class: pdf

Homework 7: due May 30 in class: pdf

Homework 8: due June 6 in class: pdf

Final Exam: Monday, June 9, 1-3pm in the usual classroom
The final exam is comprehensive and will cover all topics we discussed in class and on the homework assignments. This includes Stanley Chapters 1-6 and 8 as well as the notes on Rogers-Ramanujan identities. There will be again one question asking for definitions and statements of the main theorems as well as one True/False question that you need to justify.