UNIVERSITY OF HERTFORDSHIRE COMPUTER SCIENCE RESEARCH COLLOQUIUM presents "Understanding the Cube - Automatic Hierarchical Coordinatization of Permutation Groups" Dr. Attila Egri-Nagy (Centre for Computer Science & Informatics Research, University of Hertfordshire) 4 February 2009 (Wednesday) Lecture Theatre E350 Hatfield, College Lane Campus 3 - 4 pm Coffee/tea and biscuits will be available. Everyone is Welcome to Attend Abstract:* Despite the staggeringly huge space of possible states of the Rubik's Cube, for any scrambled state computers can give within a second a sequence of moves that restores the solved state. But does this answer the question of how to solve the Cube? Evidently not, for following the moves of one particular solution apparently gives no clue on what to do with another scrambled configuration. Here we propose that hierarchical coordinatization of permutation groups provide a way of understanding the puzzle, and show how different subgroup chains encode different algorithms and solving strategies. The coordinatization method is not restricted to permutation puzzles but can be applied wherever symmetry structures appear, both in natural and artificial systems such as crystallography, chemistry, physics, etc. The pieces of the underlying mathematical theory are really old (like Frobenius's induced representation) but here they are used in a new context, and with our newly developed software package the method is ready for practical applications. * Joint work with Prof. C. L. Nehaniv -------------------------------------------------- Hertfordshire Computer Science Research Colloquium http://homepages.feis.herts.ac.uk/~nehaniv/colloq