Instructor: Fred Goodman

Contact Information:

## Office:325G Maclean Hall |
## Email:goodman at math dot uiowa dot edu |

## Phone:Voice: 319-335-0791 |
## Paper Mail:Fred Goodman Department of Mathematics MLH The University of Iowa Iowa City, IA 52242-1419 USA |

## Office Hours:official: M, W: 2:30, F: 12:30. unofficial: anytime, night or day |
## Class Hours:## T Th 9:30-10:45,## N207 Lindquist |

Click here to read the syllabus.

Richard Brualdi, Introductory Combinatorics, 3rd Edition, Prentice Hall, 1992. This text is required. |

Assignment lists:

There will be 8 to 12 written assignments. Details will appear here as the assignments are made.

**1st assignment, due Tuesday, September 7: **Exercises from Chapter 2: 1, 3, 6, 7, 8.

**2nd assignment, due Tuesday, September 14: **Exercises from Chapter 3: Numbers 12, 14, 17-21.

**3rd assignment, due Tuesday, September 21: **Exercises from Chapter 3: Numbers 22-25, 30-33.

**4th assignment, due Thursday, September 30: **Generalizing problems from Chapter 3, we can compute circular permutations,
and "necklaces" of multisets with arbitrary multiplicities. The
method is the Polya-Burnside counting method for configurations with symmetry,
explained in class. Using this method, count circular permuations and "necklaces"
of the multiset

{2 a, 2 b, 2 c}.

**5th assignment, due Thursday, October 7: **Count necklaces with 6 beads of three colors of beads, in which
each color must be used at least once.

**6th assignment, due Tuesday, October 12: **Write computer programs to accomplish the following tasks (using
your favorite language):

1. Generate all permuations of {1,2,...,n}. Test the program for small n.

2. Compute the next permuation in lex order. Also use this to generate the list of permuations of {1,2,...,n} for small n.

3. For small n and for k <= Binomial(n, 2), compute f(n,k) = number of permuations of n of length k.

**7th assignment, due Thursday, October 21: **Chapter 5, Exercises 7-11, 14-18, 25, 26.

**8th assignment, due Thursday, November 11: **

Suppose that (a_1, a_2, ...,a_n ) is a non-negative, symmetric, unimodal sequence. Let r >= 1 and define a new sequence by b_n = Sum_{j = 0 to r-1} a_{n-j}. Show that this new sequence is also non-negative, symmetric, unimodal.

Chapter 6, Exercises 1, 4, 8, 11, 12, 14, 15, 16, 24, 28.

There will be one or two midterm exams, dates to be negotiated;
the dates will appear here when they are known. There will be a comprehensive
final exam at the time specified in the Fall, 1999 course schedule, namely
on **MONDAY, DECEMBER 13 AT 2:15 PM.** The text of the exams will appear
here after the exams have been done by all students.

Here are some exams from previous semesters, in pdf format.