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.
When: Thursday, June 13th, at 8.15 pm.
The workshop has four areas of focus.
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.
Abstract: T.B.A.
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.
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.
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:
(last update: June 13, 2019)