Combinatorial Potlatch 2019
Western Washington University
Saturday, November 23, 2019

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 or new to 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 Department of Mathematics at Western Washington University at their campus in Bellingham, Washington on Saturday, November 23, 2019.

Significant funding is being provided by the Pacific Institute for the Mathematical Sciences and the Western Washington University Department of Mathematics. Their support is gratefully acknowledged.

Schedule

All talks will be held in the Biology Building, Room 234 (BI 234), with registration and breaks nearby. See the Getting There section for exact locations and directions.

A tentative schedule follows.

• 10:00 AM Registration, Bagels and Coffee
• 11:00 AM Joris van der Hoeven, Creative Telescoping via Reductions
• 12:15 PM Lunch at The Soy House Restaurant
•   2:30 PM Riana Roux, Reconfiguration Problems in Irredundance
•   3:00 PM Cookies and Coffee
•   3:30 PM Sue Whitesides, On Hamiltonicity in Grid Graphs
•   5:00 PM Happy Hour, Twin Sisters Brewing Company

Creative Telescoping via Reductions

Creative telescoping is a fairly general technique that can be used for proving combinatorial identities. Roughly speaking, it allows for the computation of sums or integrals of the form $\sum_{k=A}^B f(k,\lambda_1,\ldots,\lambda_d), \int_A^B f(t,\lambda_1,\ldots,\lambda_d)\,dt,$ where $A,B$ are suitable limits and $f$ belongs to a suitable class of $D$-finite or holonomic functions. The technique was introduced by Doron Zeilberger and it has been generalized and optimized during the last two decades.

One recent approach to creative telescoping is based on so-called reductions". This has given rise to a series of efficient algorithms for increasingly general situations and also allowed us to gain insight into the complexity of creative telescoping. In my talk, I will briefly review these recent developments and then present an algorithm that works for general (differentially) $D$-finite functions.

Reconfiguration Problems in Irredundance

An irredundant set $D$ of a graph $G=(V,E)$ is a set of vertices such that each vertex is either isolated in the subgraph induced by $D$ or adjacent to a vertex in $V-D$ that is nonadjacent to all other vertices in $D$. The upper irredundance number IR$(G)$ is the largest cardinality of an irredundant set of $G$ and an IR$(G)$-set is an irredundant set of cardinality IR$(G)$.

To investigate how the different IR$(G)$-sets of a graph $G$ relate to one another, we consider whether it is possible to change one IR$(G)$-set into another by a sequence of steps under the condition that the every set in the sequence stays an IR$(G)$-set. This type of problem is known as a regconfiguration problem. In the model at hand we are allowed to slide one vertex in the set to an adjacent vertex during every step. We represent this reconfiguration problem as a graph, called the IR-graph of $G$, where the IR$(G)$-sets form the vertex set, and sets $D$ and $D'$ are adjacent if and only if $D'$ is obtained from $D$ by exchanging a single vertex of $D$ for an adjacent vertex in $D'$.

During this talk we will discuss the reconfiguration of different domination parameters and see how and why IR-graphs are different. We will then discuss the realizability of graphs as IR-graphs with a special focus on the esixtence and construction of IR-trees.

On Hamiltonicity in Grid Graphs

We will survey some old and new results concerning hamilton paths and cycles in grid graphs, giving a number of open algorithmic and combinatorial problems along the way. We will touch on several applications as well. This is joint work with Rahnuma Nishat.

Registration

The Combinatorial Potlatch has no permanent 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, and the sponsoring institutions provide facilities, food for the breaks and some support for speakers' travel. So expressions of appreciation to the speakers and the hosts are preferred and especially encouraged. Thanks.

Getting There

All talks will be held in the Biology Building, Room 234 (BI 234), with registration and breaks nearby. The building is in the south-central portion of the map below, marked "BI" or use the pull-down "Building" menu. Parking will be free in lot 12A, at the south end of campus, just south of West College Way. (Green area on parking map below)

Campus Map

Lodging

We have rooms reserved at the Four Points Hotel on Lakeway, for the nights of November 22 and 23.

1. Discounted rate: \\$114 (choice of either two Queen beds or one King bed).
2. Rooms are held until November 8.
3. Book with the hotel directly at 360 685 8103. (Number corrected!)
4. Make sure to mention “WWU Combinatorial Potlatch” when making your reservation.

Nearby Hotels (from WWU, organized by price)

Dining and Happy Hour

You are encouraged to join other conference participants at the various meals and other events we are planning for the day.

We have made reservations for no-host lunch and dinner at two local restaurants. We hope you can join other participants, and your guests are welcome to join us also.

Lunch: The Soy House Restaurant, 400 W Holly St, 360 393 4857

Happy Hour, Dinner: Twin Sisters Brewing Company, 500 Carolina St, 360 922 6700

Organizers

• Nancy Ann Neudauer, Pacific University, nancy (at) pacificu (dot) edu, Program Chair
• Amites Sarkar, Western Washington University, amites.sarkar (a) wwu (dot) edu, Local Arrangements Chair
Last updated: October 28, 2019, http://faculty.wwu.edu/sarkara/potlatch2019.html