MATH 245:Enumerative Combinatorics
Fall 2014, UC Davis

Lectures: MWF 3:10-4:00pm in Bainer 1128
CRN 64084
Office hours: Wednesday 5:10-6pm
Instructor: Anne Schilling, MSB 3222, phone: 554-2326,
Text: Richard P. Stanley, "Enumerative Combinatorics, Volume I" Cambridge Studies in Advanced Mathematics 49, Cambridge University Press 1997.
Prerequisites: MAT 145, 150 or equivalent; or permission by instructor
Grading: Homework presentations:
Problems will be assigned regularly in class. Students are expected to work on these problems in groups of 2-3 students. Each group should present at least one or two homework solutions in class.

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.


List of 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.