Jan 2024

CIRCA seminar February 8th

There will be a CIRCA lunchtime seminar on 8th Feb at 1pm in Theatre D of Maths.

Coen del Valle and Ruth Hoffmann will speak.

Coen’s title: It’s not always bad to be greedy
Coen’s abstract: A base for a group of permutations of a set \Omega is a subset of \Omega whose pointwise stabiliser contains only the identity permutation. In this talk we discuss a natural greedy algorithm for building a base. In 1999, Cameron conjectured that there is some absolute constant, c, such that for any primitive group, G, every greedy base for G has size at most c times that of a minimum base for G. We discuss new results towards a proof of this conjecture, namely that it holds whenever G is either symmetric or alternating, except for a class of possible exceptions. Time permitted we may also describe an interesting application in graph theory.

Ruth’s title: Composable Constraint Models for Permutation Pattern Enumeration Problems
Ruth’s abstract: I will give an introduction to permutation patterns, discuss a few pattern types as well as porperties and show on an example how constraint programming has helped breaking the current state of the art (specialised) methods to enumerate permutation pattern problems.
In particular we will look at the 1324 avoiding permutations for which to date there still is no defined growth function. We progressed the enumeration for 1324 avoiding permutations with some additional properties/constraints (namely permutations with a fixed number of inversions) and identified a unique sequence in the OEIS to this problem. This was made possible through the creation of a library of constraint models for many of the permutation pattern types, properties and statistics. This library was created with composability in mind, so that we can offer mathematicians a neat ‘copy and paste’ library from which they can create their own bespoke model for the permutation pattern problems with a selection of properties.