Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 146: Algebraic Combinatorics
Approved: 2006-02-28, A. Schilling

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Herbert Wilf, "Generatingfunctionology", 2005, $39
http://www.math.upenn.edu/%7Ewilf/DownldGF.html
Search by ISBN on Amazon: 1-56881-279-5

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

2

Chapter 1

Recurrences, generating functions

3

Chapter 1

Examples: Fibonacci numbers, binomial coefficients, Stirling numbers of second kind

1

Chapter 1

Bell numbers, exponential generating functions

6

Chapter 2

Formal power series, calculus of formal power series. Examples: Fibonacci numbers (again), Catalan numbers, derangements, Moebius function

3

Chapter 3

Exponential formula: Cards, decks, hands

5

Chapter 3

Examples: Permutations and their cycles, involutions, 2-regular graphs, connected bipartite graphs, labeled trees, money changing problem, partitions of integers, rooted trees and forests

3

Chapter 4

Sieve method, fixed points in permutations, k-cycles, Stirling numbers (again), rooks on chessboard, snake oil method

5

Chapter 4; Biggs Chapter 27

Cycle index of symmetric group, cyclic, dihedral symmetry symmetries in 3 dimensions, Polya theory