Math 353 Fall 2014 - Homework #2 Solutions
2.5.2B There are 3 Ps, 3Os, two E, N, Rs, and one I, M, S. So we want the multnomial coecient:
15
3, 3, 2, 2, 2, 1, 1, 1
And yes properispomenon is a real wo
Fall 2014: Math 353- Introduction to Combinatorics I,
Course Information Sheet
Instructor:
David Hemmer
Office:
211 or 226 (chairs office) Mathematics Building
Email:
[email protected]
Office P
Math 353 Homework #9- SOLUTIONS
1. 11.5.5B. The order of an element is the lcm of the cycle lengths. So we need a partition =
(1 , 2 , . . . , t ) so 1 + 2 + + t = 50 with the lcm of the i as large as
Math 353 Fall 2014 - Homework #7 Solutions
6.4.3BLet 2n + k have exactly n + k parts. Then the rst column in the Ferrers diagram of has exactly n + k dots,
and removing the rst column leaves the diagr
Math 353 Homework #6- Due Wednesday 10/8/14-SOLUTIONS
1. Proof: Let m be the number of partitions of n into exactly k parts (m = pk (n) = pk1 (n).
Suppose we have a solution of x1 + x2 + + xk = n with
Math 353 Fall 2014 - Homework #1 Solutions
2.2.4B There are 8! ways to put the red counters on the board. For each, we need to determine how many ways to put the
green counters on so we have a legal a
Math 353 Homework #5- Due Wednesday 10/1/14- SOLUTIONS
1. Lets dene X(n, k) to be all the possible products of n k integers taken from cfw_1, 2, . . . , k, repeats allowed.
We must show that for 1 k <
Math 353 Exam Review Sheet
The exam will cover from Chapter 2-7.5 plus other things done in class.
Definitions: You should know how these quantities are defined and be able to calculate them in small
Math 353 Homework #10- Due Monday 11/24/14- SOLUTIONS
1. 13.2.1B The regular octagon has 16 symmetries. Let r be the clockwise rotation by /4, so there are
8 rotations, namely cfw_e, r2 , r3 , . . . ,
gowf/M/f
Math 353 Midterm Exam - October 17, 2014
Instructions: You may not use any notes, books, calculators, etc. It is ok if your nal answers
include binomial coefficients and if you do not multipl
Math 353 Fall 2014 - Homework #4 Solutions
3.3.8B We are looking at 6 digit integers from 000000 to 999999. The key observation is that once we know the six digits,
there is exactly one corresponding
Name:
Math 353 Quiz #9 - November 21, 2014
1. Let G act on a set X. Give the Frobenius (Burnside) formula for the number of orbits.
number of orbits =
1
|F ix(g)|.
|G| gG
2. Dene what it means for a g
Name:
Math 353 Quiz #8 - November 10, 2014
1. Dene the center of a group G.
Z(G) = cfw_z G | zg = gzg G.
2. Let g be an element of a group G. The conjugacy class of g is . . . .?
The set of elements x