## ** 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:** Christian Gaetz

** 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.
**Problem sets**

Additional problems (possibly not yet
complete)