Math 108 - Topics in Combinatorics: Permutations, partitions and lattice paths

Instructor: Sergi Elizalde
Lectures: MWF 8:50-9:55 in Kemeny 004
X-hour: Th 9:05-9:55 (will only be used when a class needs to be moved)
Office Hours: M 10-11, W 1:30-2:30, and by appointment. Office hours will typically be in person in Kemeny 332, but I'm also happy to meet you on zoom if you tell me in advance. Additionally, you are encouraged to use the Discussions tool to ask questions or comment on other students' questions.
Email: sergi.elizalde@dartmouth.edu

Course description

This course focuses on three ubiquitous objects in enumerative combinatorics: permutations, partitions and lattice paths, as well as the connections between them. The course will cover some classical results on these topics, mixed with current research problems.

This course is aimed at graduate students (including first-year students), as well as advanced undergraduate students who have taken some combinatorics course before.

Textbook

No textbook required for this course. The material will be taken from a combination of notes, research papers, and the following books. Many of them have been put on reserve at Baker library.

[EC] Richard Stanley, Enumerative Combinatorics, Vols. I and II, Cambridge University Press. An online version Vol. I is available here.
[BS] Anders Björner, Richard Stanley, A Combinatorial Miscellany, available here.
[Bo] Miklos Bóna, Combinatorics of Permutations, Chapman-Hall and CRC Press, 2004.
[AE] George Andrews, Kimmo Eriksson, Integer partitions, Cambridge University Press, 2004.
[An] George Andrews, The theory of partitions, Cambridge University Press, 1984.
[Br] David Bressoud, Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press, 1999.
[Sag] Bruce Sagan, Combinatorics: The Art of Counting, Graduate Studies in Mathematics 210, AMS, 2020. Also available here.
[St] Richard Stanley, Notes on Permutations, available here.
[Pak] Igor Pak, Partition bijections, a survey, available here.

Other interesting related books are:

Grading and exams

There will be no exams for this course. The course grade will be based on the homework (60%) and a presentation in class (40%).

Homework policy

Homework will be assigned every other week. All the homework assignments are posted here.
You are encouraged to collaborate on the homework, but the solutions must be written individually. You must state what sources you have consulted, with whom you have collaborated, and from whom you have received help.

Although by no means required, you are encouraged to type your solutions using LaTeX. You can turn in your homework either online or on paper at the beginning of class on the due date.

Honor principle, student accessibility, and religious observances

Remember that Dartmouth's academic honor principle applies to this course.

Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Getting Started with SAS webpage; student.accessibility.services@dartmouth.edu; 1-603-646-9900) and to request that an accommodation email be sent to me in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with me to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the quarter as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me as soon as possible, or before the end of the second week of the term—at the latest, to discuss appropriate adjustments. Dartmouth has a deep commitment to support students’ religious observances and diverse faith practices.