- Vít Jelínek, Charles University – Title: On Fishburn Numbers
I will talk about various aspects of the number sequence known as the Fishburn numbers (A022493 in the OEIS). I will mention some of the many combinatorial structures enumerated by this number sequence, which include interval orders, ascent sequences, Stoimenow matchings, and certain classes of pattern-avoiding permutations. I will also talk about the generating function of these numbers and present some surprising identities involving this function. Next, I will point out several congruence identities involving the Fishburn numbers, which have been proven by number-theoretic arguments and for which no combinatorial explanation is currently known. Finally, I will talk about certain close combinatorial analogies between the Fishburn numbers and the Catalan numbers.
- Peter Winkler, Dartmouth College – Title: Permutons and Pattern Densities
Permutons, also known as doubly-stochastic measures, are limit structures for permutations (graphical grid classes are examples). For nice, large (factorial over exponential) subsets of , we have a variational principle that enables us to describe most permutations in the subset by finding the permuton that maximizes a certain entropy function.
Ideal examples of such subsets are permutations with one or more given non-zero pattern densities, for which—sometimes—we can compute the winning permuton. Can we deduce properties about smaller subsets, such as the (merely exponential) set of permutations that avoid a pattern? Maybe with your help…
Joint work with Rick Kenyon, Dan Kráľ, and Charles Radin.
Excursion and banquet
The conference banquet and excursion will be combined on Wednesday 28 June. We will visit the Reykjanes peninsula and the banquet will be at a restaurant there.
We will leave from the university at 2pm. Dinner will be at 7pm at Salthúsið in Grindavík. We will return at 10pm.
Ragnar Pall Ardal, Reykjavik University, Iceland - abstract
Elizabeth Kelley, University of Minnesota, USA - abstract
Rebecca Smith, SUNY, USA - abstract
Mike Weiner, Penn State University, USA - abstract
Alexander Woo, University of Idaho, USA - abstract
Here are some of the problems asked at the conference and the respective questioner.
William Kuszmaul - problem
Jennifer Galovich - problem