## 18.217 (FALL 2017): PARTIALLY ORDERED SETS

Prerequisites: Basic knowledge of linear and abstract algebra, such as 18.700-18.703 or 18.701-18.702. Prior knowledge of combinatorics is technically not a prerequisite. We will review some basic enumerative combinatorics as necessary.

Lectures: MWF 1:00, 2-147

Lecturer: Richard Stanley, 2-377, x3-7930, rstan [at] math [dot] mit [dot] edu (not rstan [at] mit [dot] edu)

Lecturer office hours: W 2-3 or by appointment

Grader office hours: Friday 11-12, 2-332

Text: Chapter 3 of R. Stanley, Enumerative Combinatorics, vol. 1, second edition.

Grading periodic problem sets. "Reasonable" collaboration is permitted on problem sets, but you should not just copy someone else's work or copy a solution from another source. Problem sets count 80% of the course grade.
Near the end of the semester (precise date TBA) you should hand in two problems of your own with difficulty ratings and solutions. They should be related to partially ordered sets. I certainly don't expect them to be publishable in general. Grading of these "self problems" will be based more on elegance, originality, and pedagogical value than on difficulty. The self problems count 20% of the course grade.

Problem sets. Problem sets will be due about once every two weeks. You will be asked to hand in a subset of your choosing of specified size from a list of problems. Hand in at most one part from any multipart problem unless specified otherwise. Grading of problem sets is based on the following somewhat harebrained scheme. Each problem has a difficulty factor [d], such as [3-]. This is converted into a weight w(d), as follows.

• w(1-) = 0.1, w(1) = 0.3, w(1+) = 0.5
• w(2-) = 1, w(2) = 2, w(2+) = 3
• w(3-) = 5, w(3) = 8, w(3+) = 12
• w(4-) = 18, w(4) = 25, w(4+) = 50
• w(5-), w(5): depends on solution
Each part will have ten points. Your grade on a problem will be the number of points you receive (out of 10) times the difficulty weight. The weights assume that you solved the problem from scratch. If it appears that you already had some familiarity with the problem, the weight may be reduced. To receive an A in the course, you should be able to solve successfully some of the [3-] problems.

Problem sets can be turned in during class or sent by email to the grader (gaetz@mit.edu) by the beginning of class on the due date.