Counting out symmetries by Relinde Jurrius

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Title Counting out symmetries
Lecturer Relinde Jurrius
Type Lecture
Time and location 15:15 - 16:15 @ Gezellenzaal

About Counting out symmetries

Suppose you want to open the lock to your spare bike, but you forgot its 6-digit code. Trying out all 1.000.000 combinations is infeasible by hand. But suppose you remembered that, because you always forget codes, you made this one easy: the first, third and fifth digit are equal, as are the second, fourth and sixth. This leaves only 100 combinations to try - it will take some time, but maybe it is faster than fixing the flat tire of your regular bike. In this talk we will not hunt for 6-digit codes, but we want to say something about the existence of mathematical objects called "designs". Since these are finite objects, we could, in theory, let a computer decide if a design exists for certain parameters. However, this problem becomes infeasible already for modestly large parameters.
In order to obtain partial results, we first assume the design has certain symmetries (i.e., we guess its automorphism group). The computer search can then be done "modulo symmetries". For designs, this method is contributed to Kramer and Mesner. In this talk, we will see how this method works, and discuss some of its triumphs and failures.

About Relinde Jurrius

© Ministerie van Defensie
Dr. Relinde Jurrius is an assistant professor in mathematics & operations research at the Netherlands Defence Academy. She teaches at the Faculty of Military Sciences, that provides the scientific education for officers-to-be, and does research in reliable digital communication. Her research interests are in coding theory, network coding and the connection with other branches of mathematics such as matroid theory, algebraic and finite geometry, and combinatorics.