Essays about: "Permutation groups"

Found 2 essays containing the words Permutation groups.

1. 1. Algorithmic Construction of Fundamental Polygons for Certain Fuchsian Groups

   University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

   Author : David Larsson; [2015]
   Keywords : Compact Riemann surfaces and uniformization; Fuchsian groups and automorphic functions; Hyperbolic geometry; Topological groups; Permutation groups; Computational methods; Covering spaces; branched coverings; Generators; relations; and presentations;

   Abstract : The work of mathematical giants, such as Lobachevsky, Gauss, Riemann, Klein and Poincaré, to name a few, lies at the foundation of the study of the highly structured Riemann surfaces, which allow definition of holomorphic maps, corresponding to analytic maps in the theory of complex analysis. A topological result of Poincaré states that every path-connected Riemann surface can be realised by a construction of identifying congruent points in the complex plane, the Riemann sphere or the hyperbolic plane; just three simply connected surfaces that cover the underlying Riemann surface. READ MORE

3. 2. Polya's Enumeration Theorem : Number of colorings of n-gons and non isomorphic graphs,

   University essay from Institutionen för datavetenskap, fysik och matematik, DFM

   Author : Muhammad Badar; Ansir Iqbal; [2010]
   Keywords : Generating function; Cycle index; Euler’s totient function; Unlabeled graph; Cycle structure; Non-isomorphic graph.;

   Abstract : Polya’s theorem can be used to enumerate objects under permutation groups. Using grouptheory, combinatorics and some examples, Polya’s theorem and Burnside’s lemma arederived. The examples used are a square, pentagon, hexagon and heptagon under theirrespective dihedral groups. READ MORE