ENUMERATIVE COMBINATORICS
MATH 245, course information

Meetings: MWF 3:10-4:00 PM, Wickson Hall 1020

Instructor: Prof. Jesús A. De Loera.

email: deloera@math.ucdavis.edu

Phone: (530)-754 70 29

Office hours: TBA or by appointment. My office is 3228 Mathematical Sciences Building.

Text and References: The classic book ``Enumerative Combinatorics'' Volume I, by Richard P. Stanley. I will supplement it with my own notes and exercises.

Description: The objective of this course is simply to teach you how to count (and you thought you knew since kindergarden, eh?). Indeed, enumerative combinatorics is the art of counting the number of elements of a finite set. It contains now a well-established set of tools and structures that help on carrying an exact count or how to make educated estimations. Here is an outline of the course:

1) Basic combinatorial enumeration (Permutations, Sets, MultiSets, partitions, and the Twelvefold way) and generating functions. (Chapter 1)

2) Posets, lattices and Moebius Inversion, Involutions and the Inclusion-Exclusion Principle. (Chapters 2,3)

3) Rational generating functions. (chapter 4).

• There are 100 points possible in the course. There will be 2 midterms, each worth 35 points and a 30 point final exam. The dates for the midterm exams are: October 20th and November 17. Regular homework exercises will be assigned, but they will not be collected. Instead, the exams will be partly composed of those homework problems.

• I will assign grades based on the statistical information of the points obtained by all students (I compute the mean, standard deviation, etc. and set letter grades according with those numbers). New homework exercises will be posted on my web page (see the end of the page) and announced in class too. Please there are NO make-up exams .

• You are expected to work hard outside the classroom solving exercises, reading the book, thinking about the theorems, etc. I estimate a minimum of 4 hours work at home per lecture. The most important thing is what you learn. This is achieved by doing!

HOMEWORK PROBLEMS

FIRST MIDTERM: will contain material from Stanley EC1 Chapter 1 (i.e. homeworks 1 and 2).

Here are most solutions for homework1 and that of the nasty problem 2.c of Stanley's book.

Here are most solutions for homework2.

SECOND MIDTERM: Will contain material from Stanley EC1 Chapters 2 and 3 (i.e. homeworks 3 and 4).

Here are the computer slides for my introduction to section 4.6.