Genomics, Pattern Avoidance, and Statistical Mechanics

Summary

This report documents the program and the outcomes of Dagstuhl Seminar 18451 "Genomics, Pattern Avoidance, and Statistical Mechanics".

The workshop took place from November 4, 2018 to November 9, 2018. It had 40 participants, who were researchers in theoretical computer science, combinatorics, statistical mechanics and molecular biology. It was a geographically diverse group, with participants coming from the US, Canada, Brazil, Germany, Iceland, the United Kingdom, Sweden, France, Switzerland, Hungary, Australia, and New Zealand. The workshop featured 21 talks, three of which were hourlong talks, and an open problem session.

Several collaborative projects have been started. For example, Jay Pantone Michael Albert, Robert Brignall, Seth Pettie, and Vince Vatter started exploring the topic of 1324-avoiding permutations with a bounded number of descents, disproving a 2005 conjecture of Elder, Rechnitzer, and Zabrocki related to Davenport-Schinzel sequences. Had the conjecture been affirmed, it would have implied that the generating function for 1324-avoiding permutations is non-D-finite.

At the open problem session, Yann Ponty raised the following question: what is the number of independent sets in restricted families of trees, like caterpillars or complete binary plane trees? The main motivation for this question relates to a deep connection between such independent sets and RNA designs. This question led to a new collaborative effort by Mathilde Bouvel, Robert Brignall, Yann Ponty and Andrew Elvey Price.

Sergi Elizalde and Miklós Bóna have started working on Dyck paths that have a unique maximal peak. That collaboration since extended to the area of probabilistic methods, involving a researcher working in that field, Douglas Rizzolo.

Numerous participants expressed their pleasure with the workshop and its sequence of talks. The prevailing view was that while the participants came from three different fields, they were all open to the other two fields, and therefore, they all learned about results that they would not have learned otherwise. Therefore, we have all the reasons to believe that the workshop was a success, and we would like to repeat it some time in the future.