Homework4 - σ both as an array and as a product of...

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Homework 4 Math 332, Spring 2010 These problems must be written up in L A T E X, and are due next Thursday, March 4. 1. For n 3, prove that every element of A n can be expressed as a product of one or more 3-cycles. 2. In a perfect riffle shuffle , a deck of cards is cut into two halves, which are then merged in an interleaving fashion: cut merge Note that the top card of the deck remains on top after the shuffle. (a) Write an element σ S 52 that represents a perfect riffle shuffle of a 52-card deck. Express
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Unformatted text preview: σ both as an array and as a product of disjoint cycles. (b) Explain why 8 perfect riffle shuffles will bring a 52-card deck back to its original configuration. 3. Let G be the group of symmetries of a triangular prism: ' " # $ % & Make a list of the 12 elements of G , organized into conjugacy classes. 4. Let G be the group of symmetries of the following graph: " $ & # % ' Make a list of the 48 elements of G , organized by the orders of the elements....
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This document was uploaded on 11/03/2010.

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