Doctoral Defense in Mathematics - Atli Fannar Franklín

Doctoral candidate:
Atli Fannar Franklín

Title of thesis:
Enumerating score sequences and permutations by inversions and forbidden patterns

Opponents:
Dr. Luca Ferrari, Associate Professor at the Faculty of Informatics and Mathematics, University of Florence, Italy
Dr. Robert Brignall, Senior Lecturer at the School of Mathematics and Statistics, The Open University, United Kingdom

Advisor:
Dr. Anders Karl Claesson, Professor at the Faculty of Engineering and Natural Sciences, University of Iceland

Other members of the doctoral committee:
Dr. Henning Ulfarsson, Professor at the Department of Computer Science, University of Reykjavík
Dr. Sergey Kitaev, Professor of Mathematics at the University of Strathclyde, Glasgow, Scotland
Dr. Sigurður Örn Stefánsson, Professor at the Faculty of Engineering and Natural Sciences, University of Iceland

Chair of Ceremony:
Dr. Birgir Hrafnkelsson, Professor and Head of the Faculty of Physical Sciences, University of Iceland

Abstract:
This thesis studies the enumeration of score sequences and permutations. The first paper settles a conjecture of Hanna on a recursion for the number of score sequences of a tournament, derives a closed formula, and gives a quadratic-time algorithm. The second presents generating functions for permutations with few inversions: those with as many inversions as elements, and those with a fixed number of inversions fewer than elements. The third continues on the theme of inversions, enumerating pattern-avoiding permutations by inversions for all patterns of length at most 3. The fourth and last paper explores how to obtain bounds on the number of 1324-avoiding permutations by encoding permutations as walks in a directed graph.

About the doctoral candidate:
Atli Fannar Franklín is from the north of the coutnry, but moved south to attend University of Iceland, getting a degree in both computer science and mathematics. After that he moved to Zürich to get a masters degree in mathematics at ETH. He has been active in various competition work, mostly mathematics contests and programming contests, at first as a contestant and later as an organiser.