# Pre-Conference Workshop

## Essential information:

Dates: June 13-15, 2019

Location: University of Zurich, Irchel campus. Math Institute, Building Y27, room H28

For registering to the workshop see Registration. The workshop has no registration fees.

The pre-conference workshop is meant to help people new to the subject area (students/postdocs), or those that wish to branch out to different areas, have a guided introduction to the main branches of research for Permutation Patterns. The workshop consists of four mini-courses, each with 3 lectures.

## Schedule:

## Workshop dinner:

When: Thursday, June 13th, at 8.15 pm.

## Program:

The workshop has four areas of focus.

- Algebra (Darij Grinberg)

Abstract: After reviewing the concepts and examples of rings and their homomorphisms, we will introduce the group ring of a finite group. We will then focus on the most combinatorially interesting particular case, in which the group is the symmetric group. We will first study various remarkable families of elements in the group ring of asymmetric group, such as the Young-Jucys-Murphy elements, the Tsetlin library and the Reiner-Saliola-Welker shuffles. Then we will sketch an analysis of the structure of this ring (following Young and Garsia) by way of Young diagrams and Young's seminormal basis.

- Enumerative Combinatorics (
**Jay Pantone**)

Abstract: T.B.A.

- Computational Mathematics (
**Christian Bean**)

Abstract: In this mini-course we will overview some of the automatic methods used for enumerating permutation classes. We will focus on three topics:

- The insertion encoding is a language-theoretic approach that encodes how a permutation is built up by iteratively adding a new maximum element. We will consider the case when this forms a regular language, and show how to compute the rational generating functions.

- Every permutation can be thought of as the inflation of a simple permutation. We will show how to encode this and, for permutation classes with finitely many simple permutations, compute the algebraic generating function.

- We will end by reviewing the result that all geometric grid classes have a rational generating function.

- Probability (Erik Slivken)

Abstract: Given some combinatorial class with an order parameter, *n*, what does a typical object of size *n *in that class look like? A probabilistic approach allows us to conveniently sweep pathological examples away to get a cleaner description of these objects, typically as *n* tends to infinity. We start with introducing some basic tools from probability theory. From there we explore what generating functions can tell us about the asymptotic distribution of certain statistics. Next we switch to geometric descriptions for permutation classes through various types of scaling limits. We pay particular attention to permutons.

Course Syllabi to come.

In the meantime please read Permutation Patterns: basic definitions and notation for an introduction to the subject area.

## Open problem session:

The open problem session will feature some of the submitted open problems by e-mail. Will take place in the open problem session on the first day of the Workshop, and the participants will have the opportunity to interact with

The following participants have submitted and will present open problems:

**Erik Slivken**, University of Paris VII, on "*What is the permuton limit of 4231-avoiding permutations?*".**Giulio Cerbai**, University of Florence, Firenze, on "*Transporting pattern-avoidance from ascent sequences to AV (231, {1} , {1})*".**Samuel Braunfeld**, University of Maryland, College Park, on "*Grid classes*".

## Registered participants:

(last update: June 13, 2019)

- Arnar Arnarson, Reykjavik University
- Cyril Banderier, Univ. Paris Nord
- Christian Bean, Reykjavik University
- Jacopo Borga, University of Zurich
- Mathilde Bouvel, University of Zurich
- Samuel Braunfeld, University of Maryland, College Park
- Benedetta Cavalli, University of Zurich
- Giulio Cerbai, University of Florence, Firenze
- Matteo Cervetti, University of Trento
- Dan Daly, Southeast Missouri State University
- Stoyan Dimitrov, University of Illinois at Chicago
- Michael Engen, University of Florida
- Unnar Freyr Erlendsson, Reykjavík University
- Marcel Fenzl, University of Zurich
- Valentin Feray, University of Zurich
- Darij Grinberg, University of Minnesota
- Carine Khalil, Université de Bourgogne
- Mickaël Maazoun, ENS Lyon
- Mikolaj Marciniak, Nicolaus Copernicus University in Torun
- Łukasz Maślanka, Institute of Mathematics of Polish Academy of Sciences
- Domenico Mergoni, ETHZ
- Amy Myers, Bryn Mawr College
- Émile Nadeau, Reykjavik University
- Jay Pantone, Marquette University
- Raul Penaguiao, University of Zurich
- Jean Peyen, University of Leeds
- Lara Pudwell, Valparaiso University
- Moriah Sigron, Jerusalem College of Technology
- Erik Slivken, University of Paris VII
- Rebecca Smith, SUNY Brockport
- Mariya Stamatova, University of Zürich
- Benedikt Stufler, University of Zurich
- Omar Tout, Lebanese University
- Vincent Umutabazi, Linköping University
- Gabriele Visentin, University of Zurich
- Gökhan Yıldırım, Bilkent University
- Noemi Zürcher, University of Zurich