CSE 591 / MATH 591 Combinatorial Design Theory

Contact Information:
I am located in Brickyard 444. Contact me by email at Charles.Colbourn@asu.edu as the most reliable way to reach me.

My office hours are Tuesdays 10:30-11:20, Fridays 10:00-11:00.

The class schedule is T Th 9:00-10:15. The room is BYAC 260.
Background in discrete mathematics, linear algebra, and algebra is assumed. Previous courses in combinatorics and graph theory will be useful but are not required.
We will work through the majority of the text Combinatorial Designs: Constructions and Analysis by Douglas R. Stinson (Springer, 2004).

Combinatorial design theory had its origins in finite geometry, algebra, and number theory. About a century ago, it coalesced as a field around applications in experimental design. Soon after, it became central in the evolving area of error-correcting codes for communication. Since that time, it has continued to develop deep and elegant connections with classical mathematics, while developing more and more applications.

A prototypical problem is the following. You are buying tickets for the lottery. Each ticket is a selection of 6 numbers from a set of 49 numbers. Then 6 numbers are chosen by some unpredictable process. If one of your tickets shares at least 3 numbers with those chosen, you're a winner. How many tickets do you need to buy to make sure that you're a winner?

Here's another. You are trying to assign v faculty members to committees. Every committee has exactly five members. For what values of v is it possible to make an assignment so that every two faculty members serve on exactly one committee together?

Another was discussed in the first class: See https://www.usenix.org/conference/atc13/technical-sessions/presentation/cidon "Copysets: Reducing the Frequency of Data Loss in Cloud Storage".