Professor: Eric Egge

Email: eegge at math dot (five letter school name) dot edu

Phone: 8-5988

Office Hours: Mondays from 1 pm to 2 pm, Wednesdays from 9:45 am to 10:45 am, and Thursdays from 2:30 pm to 3:30 pm, in DRL 3C3. I am also available by appointment.

Course Meetings: Mondays and Fridays from 10:30 am to noon in DRL 4N30.

Grades: Homework is worth 10%, the First Exam is worth 25%, the Second Exam is worth 25%, and the Final Exam is worth 40%.

Homework: There will be recommended homework assignments (not to be turned in) and, approximately every other week, some required homework assignments (to be turned in and graded). I encourage you to discuss the problems with each other or me, but I require the write-ups of the homework solutions to be your own. Your write-ups should be as neat as possible, with complete, appropriately organized, clearly explained solutions.

First and Second Exams: These exams will be given in class on Friday, October 10, and Monday, November 10, respectively.

Final Exam: The final exam will be from noon to 2 pm on Friday, December 12, location to be announced later. This exam will be cumulative.

This course is intended to be an introduction to enumerative combinatorics suitable for advanced undergraduates or graduate students in mathematics. The primary text for the course will be Enumerative Combinatorics, volume 1, by Richard Stanley, but in order to gain an appreciation for some recent work in the area, we will also cover selected material from Combinatorics of Permutations, by Miklos Bona, Proofs and Confirmations, by David M. Bressoud, The Symmetric Group, by Bruce Sagan, and Enumerative Combinatorics, volume 2, by Richard Stanley. A good supplemental reference for the course will be generatingfunctionology, by Herb Wilf, which available free at his website. Specific topics we will cover include basic objects in enumeration, such as generating functions, permutation statistics, Eulerian polynomials, multiset permutations, q-Binomial Coefficients, the Twelvefold Way, Stirling, Catalan, and Bell Numbers; the theory of rational generating functions, including the transfer matrix method; recent results in pattern-avoiding permutations, including the Marcus-Tardos theorem; and sieve methods, including inclusion-exclusion. As time permits, we will also study basic combinatorics of symmetric functions, including the hook length formula; and alternating sign matrices and plane partitions.

Homework Assignments

Required Homework for Friday, December 5