MATH 245:Enumerative Combinatorics
Winter 2021, UC Davis

Lectures: MWF 3:10-4:00pm in Zoom
CRN 44430
Office hours: after each class
Instructor: Anne Schilling, MSB 3222, anne@math.ucdavis.edu
Text:
  • Richard P. Stanley, "Enumerative Combinatorics, Volume I" Cambridge Studies in Advanced Mathematics 49, Cambridge University Press, Second Edition 2012
Other very useful text:
  • Bruce E. Sagan, "Combinatorics: The art of counting", Graduate Studies in Mathematics, AMS, 2020
Prerequisites: MAT 145, 150 or equivalent; or permission by instructor
Grading: Homework:
A list of problems is assigned. Two problems from the list of problems is due every second Friday (so 10 different problems in total for the quarter).
Presentation:
In addition, every second Friday we will discuss homework problems. You can team up in groups of 2-3 students and present problems during these discussions. Each student is expected to present at least one or two problems (in a group) during the quarter.
Web: http://www.math.ucdavis.edu/~anne/WQ2021/245.html

Course description

Introduction to combinatorics at the graduate level, covering the following main topics:
I. Introduction to counting (permutation statistics, twelvefold way)
II. Inclusion-Exclusion
III. Order (posets, lattices, Moebius inversion)
IV. Generating functions

The sequel to this course MAT 246 will cover symmetric functions and algebraic combinatorics.

Topics

List of Problems

Homework problems
An extension of Problem 17 can be found in:
Stanton, Dennis W.; White, Dennis E. A Schensted algorithm for rim hook tableaux. J. Combin. Theory Ser. A 40 (1985), no. 2, 211-247.
This is also related to n-cores and n-quotients of a partition.