Algebraic Combinatorics
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 not just obtain the solution from another source. Ple
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 should not just obta
3) Let G = Cn be a cycle graph on n vertices and let v0 be one of Gs vertices.
(5 points) How many critical congurations does Cn have, letting v0 be the
sink vertex?
(10 points) Describe the critical congurations of Cn . (Hint: To get started,
try writing
Algebraic Combinatorics
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 not just obtain the solution from another source. Ple
3) Recall that
of size k.
n
k
, binomial coecient, counts the number of subsets of cfw_1, 2, . . . , n
(10 points) Give an algebraic proof of the identity, i.e. use generating functions:
2
n
n
2n
=
n
k=0 k
.
(1)
(10 points) Give a combinatorial proof
Algebraic Combinatorics
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 not just obtain the solution from another source. Ple
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 either count towar
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 should not just obta
Algebraic Combinatorics
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 not just obtain the solution from another source. Ple
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 you should not