## Math 535 - Combinatorics I - Fall 2014 --- Professor: Ron Gould

 Office: E432 Math and Sciences Bldg Office Hours: 11:00-1:00PM MW or by appointment Office Phone: 404-727-7924 email: rg@mathcs.emory.edu

Text: Combinatorics - Topics, Techniques, Algorithms by Peter J. Cameron, Cambridge Univ. Press; and other reading materials supplied.

Combinatorics Hall of Fame: (1st semester)
Euler Steiner Kirkman Catalan

GRADING: Course grades will be based on a series of written assignments. Each assignment is generally due one week after completion of the material of a chapter, unless otherwise indicated. Written assignments are expected to be complete, including a statement of the problem being addressed, as well as the solution. Solutions should be written to the best ability of the student at all times. Writting style is considered important and suggestions for improvement will be made whenever deemed necessary.

The Course: The course assumes no previous knowledge of combinatorics. Thus, we build from basics. Background in linear algebra and algebra is useful. This semester the emphasis is on enumeration, but some important combinatorial structures will be introduced.

• ### Written Assignments:

(Usually due one week after chapter materials are completed in class.)

• Assignment 6: (Due Wednesday Dec. 3) From handout: page 7, problems 1.1, 1.2, 1.5, 1.7, 1.8 and page 23-24, problems 2.1, 2.2, 2.3, 2.6, 2.7, 2.13

• Practice Problems 7: From Extremal Set Theory handout II, page 53, problems 1, 3 Choose one as a bonus problem for the final assignment.

• Final Assignment of the semester: (Due by noon on Tuesday Dec. 16, 2014) Chapter 8 (pages 120-121) Problems 3, 4, 7 and from handouts: page 9 problem 1.2.7(a), 1.2.7(b)(i)(ii) and page 13, Problem 1.3.6(a), 1.3.6(b)(i)(ii)(iii) and page 58, problem 3.1.5, page 62 problem 3.2.4, page 68 problem 3.3.4.

Problem A: Prove that the Skolum construction gives a Steiner triple system.