University of Puget Sound
Saturday, November 22, 2008
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 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.]
More info, including a history and links to previous Potlatches, is at The Combinatorial Potlatch Home Page.
All talks will be held in Room 193 of Thompson Hall, with registration and breaks nearby. See the Getting There section for exact locations and directions.
- 10:00 AM Registration and Coffee
- 11:00 AM Eric Fusy, Bijective Links on Planar Maps via Orientations
- 12:00 PM Mathematical Tour of Harned Hall
- 12:45 PM Lunch
- 2:30 PM Chuck Dunn, Complete Multipartite Graphs and the Relaxed Coloring Game
- 3:30 PM Cookies, Coffee and Cokes
- 4:00 PM Ioana Dumitriu, Path Counting and the Moment Method for Random Matrices
- 5:00 PM Happy Hour, Dinner
Eric Fusy, University of British Columbia
Bijective Links on Planar Maps via Orientations
Abstract: Planar maps (graphs embedded in the plane) enjoy beautiful combinatorial properties. As shown by Tutte in the 60's, many families of planar maps have surprisingly simple enumeration formulas, which also reveal that a priori unrelated map families are equinumerous. In this talk, I will present several bijections (which rely on specific orientations on maps) to explain these "coincidences."
Chuck Dunn, Linfield College
Complete Multipartite Graphs and the Relaxed Coloring Game
Abstract: We consider the following game played on finite graph G. Two players, Alice and Bob, alternate coloring the uncolored vertices of a finite graph from a given set of colors. At each step, we require that the subgraphs induced by the individual color classes have maximum degree not exceeding a predetermined constant d. The least number of colors such that Alice has a winning strategy for this game on G is called the d-relaxed game chromatic number of G. We will examine this game on complete multipartite graphs, and highlight the interesting behavior of this parameter with this particular class of graphs.
Ioana Dumitriu, University of Washington
Path Counting and the Moment Method for Random Matrices OR Fun with Walter and Theo
Abstract: In enumerative combinatorics, the Dyck and Motzkin paths are familiar objects which have alternately tormented and elated many a graduate student (see Stanley's EC2). Statistics for these paths are thus of natural interest.
Surprisingly, one way to obtain such statistics is via random matrix theory, by exploiting a beautiful and deep connection between paths and moments of the trace; I will explain this connection in my talk. In a 2001 paper with Etienne Rassart we studied five such identities arising from random matrix results. We were able to obtain purely combinatorial arguments for three of them, but two eluded our attempts at combinatorics.
One of the tenets of EC is that any weighted counting- or generating function-like identity must have a combinatorial proof; as such, I will offer these two (and potentially, many more) Dyck and Motzkin identities as a challenge for combinatorialists.
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. Thanks.
All talks will be held in Room 193 of the Science Center, which is composed of Thompson Hall and Harned Hall. Registration, plus coffee and donuts, will be hosted in the Oppenheimer Cafe, which is located in the central courtyard of the Science Center.
Harned Hall is located close to the intersection of North 15th Street and Union Avenue in Tacoma. If you park on Union Avenue, walk straight through Harned Hall to find registration. Close to the intersection of North 14th Street and Union Avenue is a parking lot, which visitors may use free and without any kind of permit. From here you can enter Thompson Hall near the northeast corner of the parking lot and pass through to registration in the interior courtyard.
Kimberly Scotts has noted that HotelsCombined.com has a 10% rebate offer for educators. Their Tacoma list has many hotels, with the Best Western Dome Hotel Tacoma looking like a good economical choice.
- Silver Cloud Inn: waterfront hotel, about 2 miles from campus
- Hotel Murano: fancy hotel downtown, glass art theme
- There is a concentration of economy hotels near S 84th St and S Hosmer St, right off I-5. This is about 6 miles south of campus.
- UPS Admissions Office has a list of area accomodations. See the "North End" section for several nearby bed and breakfasts.
Lunch will be at The Hub, about a 10 minute drive from campus. They start serving lunch at 1:00 PM on Saturdays, but we can be seated earlier.
For those staying in Tacoma for the evening, Happy Hour will be at Engine House #9.
- Rob Beezer, University of Puget Sound, beezer (at) ups (dot) edu, Local Arrangements Chair
- Nancy Ann Neudauer, Pacific University, nancy (at) pacificu (dot) edu, Program Chair