Combinatorial Potlatch 2006
Portland State University
Saturday, November 11, 2006

The Combinatorial Potlatch is an irregularly scheduled, floating, one-day conference. It has been held for many years at various locations around Puget Sound and southern British Columbia, and is an opportunity for combinatorialists in the region to gather informally for a day of invited talks and conversation. While most who attend work in, or near, the Puget Sound basin, all are welcome.  Typically there are two or three talks given by speakers who are visiting the area, along with breaks for coffee and lunch. Many participants remain for dinner at a local restaurant or pub.

The American Heritage Dictionary defines "potlatch" as: A ceremonial feast among certain Native American peoples of the northwest Pacific coast, as in celebration of a marriage or an accession, at which the host distributes gifts according to each guest's rank or status. Between rival groups the potlatch could involve extravagant or competitive giving and destruction by the host of valued items as a display of superior wealth. [Chinook Jargon, from Nootka p'achitl, to make a potlatch gift.]

This fall's Potlatch is being hosted by the Mathematics and Statistics Department at Portland State University on Saturday, November 11, 2006.

### Schedule

• 10:00 AM Registration, Coffee and Donuts
• 11:00 AM Richard Brualdi
• 12:00 PM Lunch
• 2:00 PM Gary Gordon
• 3:00 PM Cookies, Coffee and Cokes
• 3:30 PM Matt De Vos
• 4:30 PM Happy Hour, Dinner

### The Bruhat Order for (0,1)-Matrices

We discuss the classical Bruhat order on the set of permutations of {1,2,3,...,n} and two possible extensions to more general matrices of 0's and 1's.

### Graph Polynomials For You; Graph Polynomials For Me

The Tutte polynomial of a graph is a two-variable polynomial that generalizes the very well studied one-variable chromatic polynomial. The Tutte polynomial can be generalized and specialized in other ways that give combinatorial and "practical" information about the graph. In this talk, we’ll meet the Tutte polynomial and some of its cousins. We’ll also see some applications to an expected rank polynomial that measures how reliable a given graph is. Some of this work is the product of Lafayette College’s REU (Research Experiences for Undergraduates) program.

### Sumsets and Subsequence Sums

Two vibrant and interesting topics in combinatorics are sumsets and subsequence sums in abelian groups. We will give a survey of these areas, featuring some recent results (joint with L. Goddyn, B. Mohar, and R. Samal), and an underappreciated conjecture of Schrijver and Seymour.

### Registration

The Combinatorial Potlatch has no sponsoring organization and no budget. And we like it that way. Consequently, there are no registration fees because we wouldn't know what to do with them. You are on your own for meals and lodging, speakers travel at their own expense and the host institution provides food for the breaks. So expressions of appreciation to the speakers and the hosts are especially encouraged. It also greatly helps the hosts if you can send a quick email if you plan to attend, so they can accurately plan the amount of food to order. In this case, please contact John Caughman (caughman (at) pdx (dot) edu) to confirm your attendance. Thanks.

### Getting There

All talks will be held in Cramer Hall, Room 171. (Grid location 6-B on campus map.)

"Parking Structure 1" is about a block from Cramer Hall and costs \$4 on Saturdays. This is the block marked "5" at grid location D7 on this map.

For complete information about the PSU campus: driving directions, campus maps and general parking rules then start here.

### Dining and Happy Hour

• Breakfast: The Portland Farmers Market operates on Saturday mornings, located on Park Avenue, between Harrison and Montgomery Streets, right on the PSU campus. Web site says opening time is 8:30 AM, but it may be that the start time is now really 9:30 AM. Lots of possibilities for either a healthy or indulgent breakfast.
• Lunch: Market Street Pub is the current recommendation.
• Happy Hour: We are exploring meeting at the Bridgeport Brewery. More details later.

### Organizers

• John Caughman, Portland State University, caughman (at) pdx (dot) edu, Local Arrangements Chair
• Nancy Ann Neudauer, Pacific University, nancy (at) pacificu (dot) edu, Program Chair
• Rob Beezer, University of Puget Sound, beezer (at) ups (dot) edu, Communications Chair
Last updated: November 5, 2006, http://buzzard.ups.edu/potlatch/potlatch2006.html