Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MATH 895 G200

Reading (4)

Combinatorics

Class Number: 2768

Delivery Method: In Person

Overview

  • Course Times + Location:

    Location: TBA

Description

COURSE DETAILS:

Reading Course: Topics in Combinatorics
Course Credit: 4

Overlap: MATH 821 – which was cancelled. This reading course intentionally overlaps content.
Audience: This course is intended for motivated curious students that have some exposure and interest in enumerative combinatorics. Familiarity with tree structures, counting formulas, or generating functions/series is an asset.

Prerequisite: Some familiarity with enumerative combinatorics, series manipulations (eg. (MACM 201/MATH 343/ MATH 443) and mathematical sophistication.

Exact topics will be decided in the first week and will be a function of the interests and background of the students.
Likely, topics will be drawn from:

EC2 Chapter 5: Trees and the Composition of Generating Functions
The exponential formula
Applications of the exponential formula
Enumeration of trees
The Lagrange inversion formula
Exponential structures
Oriented trees and the Matrix-Tree Theorem

EC2 Chapter 6:  Algebraic, D-Finite and Noncommutative Generating Functions Selected topics

EC2 Chapter 7: Symmetric functions
Symmetric functions in general
Partitions and their orderings
Monomial, Elementary and Complete homogeneous symmetric functions
Power sum symmetric functions
The combinatorial definition of Schur functions: 308
The RSK-algorithm, definition, consequences, and applications

AC: III COMBINATORIAL PARAMETERS AND MULTIVARIATE GENERATING FUNCTIONS
An introduction to bivariate generating functions (BGFs)
Bivariate generating functions and probability distributions

AC: IV COMPLEX ANALYSIS, RATIONAL AND MEROMORPHIC ASYMPTOTICS
Generating functions as analytic objects
Analytic functions and meromorphic functions
Singularities and exponential growth of coefficients 

AC VII APPLICATIONS OF SINGULARITY ANALYSIS
Simple varieties of trees and inverse functions
Tree-like structures and implicit functions

Grading

  • Participation 20%
  • Presentations 80%

NOTES:

Students will be assigned readings and be responsible to present them in class. Each session will consist of a 50 minute presentation, followed by a general discussion and problem session. In person participation will be graded.

Materials

MATERIALS + SUPPLIES:

Topics and Text References:
We will follow sections from the following books, and other sources.

  • Enumerative Combinatorics II by Richard Stanley volume 2
  • Analytic Combinatorics by Flajolet and Sedgewick

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.