Posted by: jonglapa | December 8, 2008

My Reading Project

My reading project was on the article, “Groups of Perfect Shuffles.” It deals with the structure of groups in shuffling (not just the normal way) various decks of cards. Check the link to see my report on the article.

reading-project-final1

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Responses

  1. What a fascinating topic for a paper! I was very interested to see the list of what’s known and what’s unknown. It’s very open to compute investigation, and I wonder what data has been collected this way. I’m sure you read the blog posts on this blog about card tricks with interest! Group theory really is everywhere in the world around us — including every time you shuffle a deck of cards!

    The author in the paper you read analysed these groups by looking at how they fit inside S_n. We also did this in the class for matrix groups over finite fields and symmetry groups of polyhedra. You may be noticing a pattern. In fact, every single finite group is isomorphic to a subgroup of some S_n for some n. You saw this in one of the exploratory problems: you can associate to any element of a group a permutation by looking at how it permutes the other elements of the group by multiplication. In other words, you can read it from the multiplication table. This is one reason S_n is so important.

    I wonder if you could also invent other types of shuffles and see what types of groups those generate. Did the author give references for this?


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