Joint ICE-TCS@Reykjavik University/GSSI virtual seminar series: Henning A. Ulfarsson

Combinatorial Exploration: guided by humans, proven by computer

  • 7.4.2020, 13:30 - 14:10

On Tuesday 7 April, we will start a new, virtual, joint ICE-TCS@Reykjavik University/GSSI virtual seminar series.

The first talk will be given by Henning A. Ulfarsson (ICE-TCS, Department of Computer Science, Reykjavik University; https://permutatriangle.github.io) at 13:30 GMT (15:30 Italian time). The talk will last approximately 40 minutes and will describe some very neat work that Henning and his coworkers have been carrying out for a few years on the automation of proofs of combinatorial results.

For the first talk in this series, we will experiment with jitsi (https://jitsi.org/). You will receive a web link to join the talk ten minutes before the start of the talk.

The talk is open to everyone and if you want to join, please fill out the form so that we can send the link to you  https://forms.gle/UP7F8dwWjNYPBqqY6  

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# Combinatorial Exploration: guided by humans, proven by computer

## Speaker: Henning Ulfarsson, Department of Computer Science Reykjavik University
https://permutatriangle.github.io

## Abstract

Combinatorial objects can be found throughout mathematics. Permutations, words, tableaux, and other such families of objects often play a role in diverse subfields of mathematics, physics and computer science. When the structure of the object under investigation is known there are well-established tools, such as symbolic and analytic combinatorics, that derive an enumeration, asymptotics, and the ability to randomly generate instances of the objects.

However, the initial step from a definition of the object to a structural description is often ad-hoc, human-staring-at-a-blackboard type of work. This is the gap Combinatorial Exploration attempts to fill. It requires a computer-readable definition of the object and strategies on how to manipulate, break-down and reason about the domain. We have implemented Combinatorial Exploration in Python and applied it to several combinatorial objects, such as permutations, set partitions and words. In this talk we will focus on permutations and show how we have found structural descriptions of so-called 'permutation classes' which were either unknown or were the main results of research papers, some as recent as 2018.



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