Tag Archives: symmetries

Schreier-Sims Algorithm

Introduction Throughout this article, we let G be a subgroup of generated by a subset  We wish to consider the following questions. Given A, how do we compute the order of G? How do we determine if an element lies in G? Assuming , how … Continue reading

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Burnside’s Lemma and Polya Enumeration Theorem (2)

[ Acknowledgement: all the tedious algebraic expansions in this article were performed by wolframalpha. ] Counting Graphs One of the most surprising applications of Burnside’s lemma and Polya enumeration theorem is in counting the number of graphs up to isomorphism. … Continue reading

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Burnside’s Lemma and Polya Enumeration Theorem (1)

[ Note: this article assumes you know some rudimentary theory of group actions. ] Let’s consider the following combinatorial problem. Problem. ABC is a given equilateral triangle. We wish to colour each of the three vertices A, B and C by … Continue reading

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Casual Introduction to Group Theory (1)

Introduction Last year, I created a blog which was supposed to introduce concepts to abstract algebra in a systematic manner. Though I was reasonably happy with the end result, I got the sneaky feeling upon completion that the end product … Continue reading

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