Course 18.312: Algebraic Combinatorics
Lecture Notes # 10 Addendum by Gregg Musiker
(Based on Lauren Williams Notes for Math 192 at Harvard)
February 25th - 27th, 2009
1
Introduction to Partitions
A partition of n is an ordered set of positive integers =
Course 18.312: Algebraic Combinatorics
Homework # 8
Due Wednesday April 8, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that you shoul
Course 18.312: Algebraic Combinatorics
Homework # 9
Due Tax Day, Wednesday April 15, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that
Course 18.312: Algebraic Combinatorics
Homework # 10
Due Friday May 1, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that you should no
Course 18.312: Algebraic Combinatorics
Lecture Notes # 1 Addendum by Gregg Musiker
February 4th - 6th, 2009
1
Recurrence Relations and Generating Functions
Given an innite sequence of numbers, a generating function is a compact way of
expressing this data
Course 18.312: Algebraic Combinatorics
Lecture Notes # 7 Addendum by Gregg Musiker
February 18th, 2009
1
Mbius Function on Posets
o
This material closely follows selections from Chapter 3 of Enumerative Combina
torics 1 by Richard Stanley.
1.1
New Posets
Course 18.312: Algebraic Combinatorics
Lecture Notes # 6 Addendum by Gregg Musiker
February 17, 2009
1
Partially Ordered Sets II: Dilworths Theorem
Denition. An anitchain A of a poset P is a subset of elements of P such that
for all x, y A, x y and y x.
W
Course 18.312: Algebraic Combinatorics
HW # 6
Will be collected March 20, 2009
Due to the length of MT # 1, I am grading the midterm as if it were out of 55
points, and assigning problems #3 and #4 in lieau of homework this week. This
problem set will eit
Course 18.312: Algebraic Combinatorics
Homework # 7
Due Wednesday April 1, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that you shoul
Course 18.312: Algebraic Combinatorics
In-Class Exam # 2
April 17, 2009
Open notes. Closed Friends and Enemies. No calculators, computers, I-po ds, or
Zunes. Please explain your reasoning or metho d, even for computational problems.
You may do the problem
Course 18.312: Algebraic Combinatorics
In-Class Exam # 1
Friday The Thirteenth, March 2009
Open bo oks. Closed Friends and Enemies. No calculators, computers, I-po ds, or
Zunes. Please explain your reasoning or metho d, even for computational problems.
Yo
Course 18.312: Algebraic Combinatorics
Problem Set # 2
Due Wednesday February 18th, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that
Course 18.312: Algebraic Combinatorics
Problem Set # 5
Due Wednesday March 11th, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that you
Course 18.312: Algebraic Combinatorics
Problem Set # 4
Due Wednesday March 4th, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that you
Course 18.312: Algebraic Combinatorics
Problem Set # 3
Due Wednesday February 25th, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that
Course 18.312: Algebraic Combinatorics
Problem Set # 1
Due Wednesday February 11th, 2009
You may discuss the homework with other students in the class, but please write
the names of your collaborators at the top of your assignment. Please be advised
that